Beckford's 67th minute strike was only United's fourth goal in seven pre-season games and secured their first win since the opening friendly at Shelbourne.
The visitors were second best in the opening period, as League Two outfit Darlington missed a succession of gilt-edged chances, but Leeds improved after the break, when the hosts rarely threatened.
Boss Dennis Wise probably didn't learn an awful lot from last night's clash as his line-up reflected what a difficult summer it has been at Elland Road.
Less than two weeks before their opening League One fixture, at Tranmere, United included just five senior signed-on players in their starting line-up - Jonathan Howson, Beckford, Tresor Kandol, Seb Carole and youngster Scott Gardner, while fellow full-back Ben Parker, has been offered a deal for the forthcoming campaign.
Watford keeper Scott Loach was one of five players in the first 11 hoping to earn a contract, alongside Matt Heath, Alan Thompson, Curtis Weston and Rui Marques.
United were without injured stalwarts Eddie Lewis (ankle) and Frazer Richardson (hamstring), plus trialist Leon Constantine (ankle) and Richard Cresswell wasn't included as he nears a move to Hull.
Wise opted to leave out Jonathan Douglas and David Prutton, who are both suspended for the opening league game.
Captain Thompson was the stand-out for United, despite one defensive howler which almost gifted Darlington a goal early on.
Howson - who created United's winner - also caught the eye in midfield, while Kandol was strong in the air and Beckford caused the home defence problems, particularly in the second-half.
Gardner also looked lively for United on the right side of defence, but Wise must be concerned at the number of chances Darlington - who now haven't scored in four friendlies against League opposition - created in the second quarter.
Leeds were stronger defensively after the break, but - though Loach wasn't particularly tested - Darlington were allowed several free headers, which better opposition would have taken advantage of.
United created only a limited number of chances, but did have three efforts cleared off the line.
The first of those came after just eight minutes, when Kandol headed Thompson's free kick over keeper Andy Oakes, but Tim Ryan did brilliantly to get back and hook clear, Heath heading across goal from the resulting corner. Ryan repeated the feat - though less spectacularly - from a Kandol header just before half-time and Steve Foster blocked Howson's shot in the second half.
Another Thompson free kick, which beat Oakes, flashed just wide and Howson was off target with a powerful shot, but that was the extent of United's first-half chances. Darlington made a tense start, but grew in confidence and with better finishing could have been a couple of goals in front at the break.
The hosts applied plenty of pressure, with Tommy Wright fluffing three chances in as many minutes.
The north east side forced their first chance after just four minutes, when Foster headed just over from Kevin McBride's corner.
It took them until mid-way through the first-half to threaten again, but they spent the rest of the period well on top.
First Thompson's careless backpass almost put McBride in, but Loach reacted quickly to clear the danger, then United old boy Julian Joachim's effort was hacked clear by Parker.
Wright should have scored when he was put through clear on goal, but he managed to totally scuff his shot, prodding the ball weakly straight to Loach.
Seconds later Parker's great tackle whipped the ball clear from Wright and from the resulting corner the striker's header looked goal-bound, but Loach produced a fine save, diving to his left.
Darlington forged another opportunity when Neil Austin's cross picked out Joachim in front of goal, but he powered his header just over.
Joachim was denied again five minutes before the break, when he shot straight at Loach.
The second half was a different story as United looked more assured at the back and played with greater composure and enthusiasm in the opposition half.
Early on Beckford went close and then Howson shot well over, before Wright missed yet another chance for Darlington when he headed over after good work by trialist Craig Nelthorpe.
After Foster had denied Howson, the breakthrough finally came on 67 minutes.
Howson broke through the middle and threaded a neat pass between two defenders to Beckford, who finished coolly past Oakes.
The hosts should have equalised almost immediately, on a rare second-half attack, but Joachim was well wide from in front of goal on the edge of the area.
The goal lifted United's confidence and they created more opportunities as Kandol's shot produced a low save by Oakes and the same player headed over from the resulting corner.
United nearly finished with a flourish, but Kandol's ferocious shot in injury time brought a flamboyant save from Oakes.
This was United's fourth win in as many pre-season visits to Darlington's new ground since they were relegated from the Premiership.
The crowd of 3,270 included 1,467 visiting fans - a sizable percentage of them shedding their footwear for choruses of "shoes off if you hate Ken Bates".
Darlington: Oakes, Austin, White, Foster, Ryan, Joachim, Ravenhill, McBride, Nelthorpe, Wright, Blundell. Used subs Miller, Wainwright, Cummins, Purdie, Burgess, Reay, Harty, McMaster.
Leeds United: Loach, Gardner, Rui Marques, Heath, Parker, Howson, Thompson (Delph 79), Weston, Carole (Baily 83), Kandol, Beckford. Unused subs Elliott, Hamman, Madden.
Referee: Clive Oliver.
The visitors were second best in the opening period, as League Two outfit Darlington missed a succession of gilt-edged chances, but Leeds improved after the break, when the hosts rarely threatened.
Boss Dennis Wise probably didn't learn an awful lot from last night's clash as his line-up reflected what a difficult summer it has been at Elland Road.
Less than two weeks before their opening League One fixture, at Tranmere, United included just five senior signed-on players in their starting line-up - Jonathan Howson, Beckford, Tresor Kandol, Seb Carole and youngster Scott Gardner, while fellow full-back Ben Parker, has been offered a deal for the forthcoming campaign.
Watford keeper Scott Loach was one of five players in the first 11 hoping to earn a contract, alongside Matt Heath, Alan Thompson, Curtis Weston and Rui Marques.
United were without injured stalwarts Eddie Lewis (ankle) and Frazer Richardson (hamstring), plus trialist Leon Constantine (ankle) and Richard Cresswell wasn't included as he nears a move to Hull.
Wise opted to leave out Jonathan Douglas and David Prutton, who are both suspended for the opening league game.
Captain Thompson was the stand-out for United, despite one defensive howler which almost gifted Darlington a goal early on.
Howson - who created United's winner - also caught the eye in midfield, while Kandol was strong in the air and Beckford caused the home defence problems, particularly in the second-half.
Gardner also looked lively for United on the right side of defence, but Wise must be concerned at the number of chances Darlington - who now haven't scored in four friendlies against League opposition - created in the second quarter.
Leeds were stronger defensively after the break, but - though Loach wasn't particularly tested - Darlington were allowed several free headers, which better opposition would have taken advantage of.
United created only a limited number of chances, but did have three efforts cleared off the line.
The first of those came after just eight minutes, when Kandol headed Thompson's free kick over keeper Andy Oakes, but Tim Ryan did brilliantly to get back and hook clear, Heath heading across goal from the resulting corner. Ryan repeated the feat - though less spectacularly - from a Kandol header just before half-time and Steve Foster blocked Howson's shot in the second half.
Another Thompson free kick, which beat Oakes, flashed just wide and Howson was off target with a powerful shot, but that was the extent of United's first-half chances. Darlington made a tense start, but grew in confidence and with better finishing could have been a couple of goals in front at the break.
The hosts applied plenty of pressure, with Tommy Wright fluffing three chances in as many minutes.
The north east side forced their first chance after just four minutes, when Foster headed just over from Kevin McBride's corner.
It took them until mid-way through the first-half to threaten again, but they spent the rest of the period well on top.
First Thompson's careless backpass almost put McBride in, but Loach reacted quickly to clear the danger, then United old boy Julian Joachim's effort was hacked clear by Parker.
Wright should have scored when he was put through clear on goal, but he managed to totally scuff his shot, prodding the ball weakly straight to Loach.
Seconds later Parker's great tackle whipped the ball clear from Wright and from the resulting corner the striker's header looked goal-bound, but Loach produced a fine save, diving to his left.
Darlington forged another opportunity when Neil Austin's cross picked out Joachim in front of goal, but he powered his header just over.
Joachim was denied again five minutes before the break, when he shot straight at Loach.
The second half was a different story as United looked more assured at the back and played with greater composure and enthusiasm in the opposition half.
Early on Beckford went close and then Howson shot well over, before Wright missed yet another chance for Darlington when he headed over after good work by trialist Craig Nelthorpe.
After Foster had denied Howson, the breakthrough finally came on 67 minutes.
Howson broke through the middle and threaded a neat pass between two defenders to Beckford, who finished coolly past Oakes.
The hosts should have equalised almost immediately, on a rare second-half attack, but Joachim was well wide from in front of goal on the edge of the area.
The goal lifted United's confidence and they created more opportunities as Kandol's shot produced a low save by Oakes and the same player headed over from the resulting corner.
United nearly finished with a flourish, but Kandol's ferocious shot in injury time brought a flamboyant save from Oakes.
This was United's fourth win in as many pre-season visits to Darlington's new ground since they were relegated from the Premiership.
The crowd of 3,270 included 1,467 visiting fans - a sizable percentage of them shedding their footwear for choruses of "shoes off if you hate Ken Bates".
Darlington: Oakes, Austin, White, Foster, Ryan, Joachim, Ravenhill, McBride, Nelthorpe, Wright, Blundell. Used subs Miller, Wainwright, Cummins, Purdie, Burgess, Reay, Harty, McMaster.
Leeds United: Loach, Gardner, Rui Marques, Heath, Parker, Howson, Thompson (Delph 79), Weston, Carole (Baily 83), Kandol, Beckford. Unused subs Elliott, Hamman, Madden.
Referee: Clive Oliver.