Jacob Mellis opened the scoring for the Tykes in the fourth minute before Chris O'Grady added the second five minutes after the break. Hull's final game of the regular season, in which a win will still mean automatic promotion, is at home to Cardiff next Saturday.
This result means Barnsley are now three points clear of Peterborough in the relegation zone ahead of their final game of the season against Huddersfield.
Wolves remain in the bottom three as their 2-1 defeat by 10-man Burnley at Molineux sparked a pitch invasion by disgruntled fans.
Danny Ings and Martin Paterson both scored for the visitors before Burnley defender Michael Duff was sent off for his second yellow card of the game. Nouha Dicko pulled a goal back for Wolves two minutes before the final whistle but it was too little, too late, as Wolves remain second-bottom with one game against promotion-hunting Brighton still to play.
A late goal at Elland Road saw 10-man Brighton beat nine-man Leeds to secure a play-off place for Gus Poyet's side in an ill-tempered match. Will Buckley opened the scoring for Brighton in the 10th minute, with Leeds midfielder Rodolph Austin shown red shortly after following an off-the-ball collision with Ashley Barnes.
Brighton's Inigo Calderon was sent off midway through the second half for a challenge on El-Hadji Diouf, who scored the resulting penalty before being sent off himself after appearing to abuse the away fans following the goal. Jose Ulloa then had the final word as he headed a late winner for Brighton.
Meanwhile, Crystal Palace played out a 1-1 draw at Blackburn as they missed to chance to all but secure their play-off place, while James Vaughan scored a hat-trick as Huddersfield allayed their relegation fears with a 3-1 win over already relegated Bristol City.
Bolton held champions Cardiff to a 1-1 draw at the City Stadium to take the shine off their league winners trophy presentation and elsewhere, Nottingham Forest beat Millwall 1-0 to remain just outside of the play-off places on goal difference to sixth-placed Bolton thanks to Greg Halford's eighth-minute score.
Middlesbrough and Charlton played out a mid-table 2-2 draw at the Riverside, while Ipswich moved level on points with opponents Birmingham following their 3-1 home win, and Blackpool claimed a 2-1 home win over Derby but it could have been more as Tom Ince missed a penalty in the first half.
- Sports & Recreation