Matty Fryatt netted a hat-trick as Hull won 3-1 at home to Barnsley on Tuesday night to keep their slim Championship play-off hopes alive.
Barnsley can finally put their relegation fears to bed despite an eighth defeat in 10 league matches.
Former Leicester striker Fryatt took his tally for the season to 15 with two close-range strikes in the first half followed by a superb solo goal late in the game at the KC Stadium.
Nick Barmby's side could still catch fifth-placed Blackpool or Cardiff who are just below them if they win their last two matches and either one of those two teams fails to take another point. However, both have a superior goal difference over the Tigers, who also trail sixth-placed Middlesbrough by two points.
Meanwhile, Keith Hill's charges, who responded through Jim McNulty, are no longer looking over their shoulders following Coventry's defeat against Millwall.
Driving hail accompanied the opening few minutes of the match and it appeared to play havoc with both sides' ability to find a team-mate.
Liam Rosenior conspired to give the ball straight to Jim O'Brien but he lost his footing, conceding a throw-in in the process.
Craig Davies earned an early corner with an attempted cross which flicked off the legs of Corry Evans, but Lee Collins could only get slight contact on McNulty's looping delivery and Vito Mannone comfortably claimed.
Fryatt produced an uncharacteristically glaring miss moments later as he collected Robert Koren's precise pass before shooting tamely at David Button.
The Tigers were first to find their rhythm and when Robert Koren found Cameron Stewart on the edge of the box, the quick-thinking winger played an excellent backheel for Fryatt but Stephen Foster snuffed out the danger.
Another chance came and went in the 15th minute as Stewart laid the ball off for Evans and his first-time shot cracked the outside of Button's left upright.
It took until midway through the opening half for the Tykes to get their first clear sight of goal. Former City midfielder Nathan Doyle chipped in a free-kick, Foster nodded it on and Andy Gray's toe-poked effort forced Mannone into his first meaningful save.
Controversy stirred in the 28th minute as Andy Dawson raced clear on the left-hand side only to be halted in his tracks by referee Paul Tierney's whistle.
However, howls of derision almost turned to hoots of delight as Tom Cairney's free-kick - for which the play had been stopped - was fumbled into the path of Fryatt, who was somehow denied by the recovering Button.
The breakthrough finally came eight minutes before the break as Stewart's low cross found Fryatt and he stabbed home from close range as the visiting defence appealed for offside.
Fryatt netted his second goal on the stroke of half-time, Richard Garcia providing a delivery which needed only a touch to turn in.
Hill's men made more of a fist of it in the second half, helped in part by Hull's apparent lack of urgency in the early stages.
Davies flashed a shot wide and Scott Wiseman's cross, which appeared to strike Cairney's hand, helped the travelling fans find their voice.
And the visitors gave them what they wanted with just their third goal in 10 matches, McNulty ghosting across to the near post to nod in Gray's corner with 16 minutes to play.
Substitute Josh King almost replied immediately for Hull but his shot deflected into the side-netting and, somehow, he was not even awarded a corner for his troubles.
A flurry of corners offered Barnsley some hope of a late leveller but City put the game to bed when Fryatt jinked past two players and coolly found the bottom corner to cap a superb display in the 83rd minute.