Hull 3-1 Barnsley
Matt Fryatt's hat-trick kept alive Hull's slim hopes of reaching the play-offs while other results ensured Barnsley cannot be relegated.
Fryatt struck twice in quick succession with almost identical finishes from close range to give Hull a deserved lead after a dominant first half.
Andy Gray headed in at the near post from Reuben Noble-Lazarus's corner to reward Barnsley's second-half pressure.
But Fryatt added a fine solo effort for his third to ensure victory.
However, Hull are six points behind the play-off places so they will need to win both their remaining two games and hope Blackpool or Cardiff fail to take another point.
Both sides have a superior goal difference to the Tigers, who also trail seventh-placed Middlesbrough by two points.
Former Leicester striker Fryatt took his tally for the season to 15 as he helped to extend Barnsley's poor run to only one victory from 13 matches and no away wins in nine.
The home side controlled the first half and saw Corry Evans' first-time shot hit the outside of a post, while Fryatt was twice denied by Barnsley goalkeeper David Button before opening the scoring.
Barnsley improved after the interval, helped by Hull's lack of urgency, with Craig Davies going close before Gray headed in only his side's third goal in 10 matches.
A flurry of corners offered Barnsley some hope of a late leveller before Fryatt put the game to bed.
Hull boss Nicky Barmby: "Believe it or not, we weren't thinking about it (the play-offs).
"We wanted a good performance and a good win. We owe it to the fans to finish on a positive note and you've seen that.
"The first half was excellent, how I know we can play. We created a number of opportunities. Second half showed that no team has a God-given right to dominate for 90 minutes. We knew Barnsley would come at us, and to their credit they did, and they pegged us back.
"We knew if we weathered the storm we could hit them on the break and we did."
Barnsley boss Keith Hill: "Our form has been awful since the turn of the year. When I came in we were relegation favourites, but we've overcome that and we've done it within our financial structure.
"Our football club and the fans should be proud of that.
"It leaves a slightly bitter taste because our form up to January was excellent and gave us encouragement in terms of what we thought we were building."