Former Leeds duo Michael Duberry and Ian Westlake lined up against their old club, Duberry captaining Wycombe and Westlake recovering from a hamstring injury and lasting until just after the hour.
Becchio scored his first goal of the season to fire the club to a narrow win in their first ever visit to Adams Park.
United toiled through the first hour of the League One clash, but Becchio's blistering second-half strike gave Leeds three points.
Wycombe stifled their visitors before the break, creating most of the chances and troubling United's defence with their variety in attack.
But so far this season Wycombe have scored just twice in what has been a baptism of fire for the league's new boys.
Chris Zebroski's brace during the opening day defeat at Charlton is the total to date, leaving the side without a point and just one place above bottom club Southampton.
Zebroski should have opened the scoring after 15 minutes when he drove Matt Phillips' cut-back straight at Shane Higgs from the edge of the box, and John Mousinho failed to apply the slightest touch that was needed to turn another Phillips delivery into the net.
United, however, came closest to scoring when Jermaine Beckford, who was booked for dissent in the first half, turned and drove a shot against the post in the 16th minute after getting the wrong side of Luke Oliver, and his wayward finish wasted a good through ball from Robert Snodgrass 12 minutes before the break.
Leeds looked more dominant after the restart, however, and Becchio settled the match when he found the net with a sharp effort from about 20-yards after slipping his marker Duberry, drilling the ball beyond the reach of Scott Shearer.
United continued to control the game after taking the lead and came very close to a late second when Michael Doyle turned on the edge of the box and hit a powerful shot just wide.
Wycombe could have snatched a draw at the death but Higgs reacted brilliantly to turn substitute Stuart Green's shot onto a post.
Right-back Jason Crowe suffered an ankle injury but should be fit for Tuesday night's game at Walsall.
Shane Higgs: Higgs' top-class save at the very end was the difference between a narrow win and a less-than-inspiring draw for United. There were no complaints about his handling either - 8/10
Jason Crowe: Caught out of position twice early on, occasions when Wycombe could and should have scored. Balanced that later with some useful forward play - 6/10
Patrick Kisnorbo: Wycombe's direct tactics were a problem for United's centre-back pairing, who are not the tallest of defenders, but Kisnorbo's dominance grew as the match wore on - 7/10
Rui Marques: Made hard work of his first-half tussle with Harrold but cruised through the second 45 minutes, save for a late error which might have been costly - 6/10
Andrew Hughes: Tied up Zebroski fairly tightly, negating a player who was liable to cause United problems. But as with Crowe, he took a good hour to figure in an attacking sense - 6/10
Robert Snodgrass: Not his best performance, and failed to cause significant havoc on the right. Made one killer pass and pursued everything, but little came off - 6/10
Jonathan Howson: Forced to chase the ball thanklessly until United's midfield got a grip of the game at the start of the second period. After that, his use of possession was much improved - 6/10
Michael Doyle: Scarcely noticeable before the break as Wycombe dictated the game, but he and Howson manipulated Wanderers in the lead up to the hour mark, forcing a breakthrough - 7/10
Bradley Johnson: Could not find a way into the match until, with the benefit of the half-time interval, he discovered a spark from somewhere. Far more influential in the last half-hour of play - 6/10
Luciano Becchio: Smothered by Duberry and Oliver for 45 minutes before gaining some welcome breathing space and changing the game with a terrific strike - 7/10
Jermaine Beckford: The striker showed a positive and negative side with a shot against the post and a booking for dissent, but his pace and movement slowly took its toll on the home side - 7/10
Substitutes; David Prutton (for Snodgrass, 84) - 5/10 Enoch Showunmi (for Becchio, 90) - 5/10
Subs Unused: Ankergren, Michalik, Robinson, Grella, Kilkenny.
Wycombe Wanderers: Shearer, Smith (Green 77), Duberry, Oliver, Woodman, Mousinho, Westlake (Pittman 62), Montrose, Mousinho, Phillips, Harrold (Beavon 73), Zebroski.
Subs Unused: Young, Johnson, Westwood, Spiller.