United head coach Garry Monk named an unchanged side following the 1-0 victory over Derby County for the trip to Oakwell.
Chances were limited for both sides early into the match, Adam Davies did well to gather Pablo Hernandez’s cross turned shot and Rob Green was called into action to save Ryan Kent’s dangerous low cross.
United took the lead in the 18th minute, Hernandez countered well to win Leeds a corner. The Spaniard delivered and Wood volleyed home into the bottom right corner.
Leeds continued to press for a second goal winning a series of corners, Wood went close to putting United further ahead when he was found at the back post by Hernandez, but the striker saw his effort cleared off the line.
Souleymane Doukara was next to go close in the 26th minute, he turned superbly before firing on goal and Davies was at full stretch to tip the ball around the post for a corner.
Barnsley then threatened from a set-piece, Ryan Kent delivered and Angus MacDonald saw his header saved really well by the diving Green.
From another set-piece the Tykes again went close, Kent again delivered, Marc Roberts got his head to it but couldn’t find the target, with his header going over the crossbar.
The hosts however did level before the break, Adam Armstrong crossed and Tom Bradshaw headed home into left corner.
MacDonald then had another opportunity from a Tykes corner, however this time he was unable to find the target.
Half Time: Barnsley 1-1 Leeds United
Barnsley resumed after the break from where they left off in the first half and took the lead three minutes into the second period when Kent found the bottom left corner of the net with a driven low strike from the angle of the box.
Tykes captain Conor Hourihane then extended the Red’s lead. Josh Scowen was tripped by Roofe 25 yards from goal and Hourihane found the top left corner from the set-piece.
Bradshaw then went close following James Bree’s cross, but the striker was unable to extend his goal tally for the evening.
United were given a lifeline in the 67th minute, Marc Roberts was penalised for handball after pressure from Wood and Leeds were awarded a penalty. The New Zealand striker stepped up to take the penalty and was successful from 12 yards.
Hernandez then did well in the Reds penalty area, he cut inside before having his shot blocked, the ball fell to Leeds substitute Eunan O’Kane, but he could only blaze his effort over the bar.
Bradshaw then had an opportunity when he went through on goal, but Green made a really brave save to keep Leeds in it.
Doukara then showed good control on the edge of the box before firing a half volley on goal, but Davies denied him.
Leeds then had a great chance in the first minute of added time, Stuart Dallas put in a really teasing cross and Roofe at the back post couldn’t finish the chance.
Dallas then tried a spectacular effort from the edge of the box, but his effort went just inches wide of the top left corner, as United suffered a first defeat since December.
Full Time: Barnsley 3-2 Leeds United
Barnsley: Davies, Bree, Jones, Roberts, MacDonald, Scowen, Hourihane, Watkins, Kent, Bradshaw (Hammill 78), Armstrong (Williams 90).
Subs not used: Townsend, White, Jackson, Moncur, Payne.
United: Green, Berardi, Bartley, Ayling, Coyle, Bridcutt (Dallas 84), Hernandez, Vieira (O'Kane 58), Roofe, Doukara, Wood.
Subs not used: Silvestri, Antonsson, Phillips, Denton, Mowatt.
Booked: Hourihane, Watkins, Scowen, Armstrong (Barnsley), Bartley, Roofe, O’Kane (Leeds)
Referee: M. Dean
Attendance: 17,817 (5,241 Leeds)