Palace went into the relegation tussle at Selhurst Park needing one point to stay up and took the upper hand from the start with a goal inside three minutes from Wilfried Zaha.
Christian Benteke gave Palace a two-goal cushion before halftime when he headed home Jason Puncheon’s corner in the 34th minute for his 15th league goal.
Palace, with Luka Milivojevic adding an 85th-minute penalty and substitute Patrick van Aanholt completing the rout in stoppage time, climbed to 13th on 41 points leaving Hull in 18th with 34, four adrift of 17th-placed Swansea with one match remaining.
Taking an early lead was just the tonic for Palace with Hull then needing at least two goals as the home side settled into a counter-attacking game.
Michael Dawson headed an innocuous ball back towards fellow central defender Andrea Ranocchia, who completely missed his effort to clear and the alert Zaha pounced on the loose ball to race into the box and steer it past Jakupovic.
Palace’s James Tomkins headed just wide from a corner soon after but Hull failed to heed the warning and Benteke beat Harry Maguire to Puncheon’s next corner and powered home a header.
Hull’s goalkeeper denied Benteke a second goal later in the first half, following a fine sweeping counter-attack from the home side with Johan Cabaye laying off the final pass to the big striker only for Jakupovic to block his close-range shot.
Hull might have had a penalty when Puncheon appeared to deflect a free kick from Kamil Grosicki with his arm but referee Martin Atkinson indicated a corner for the visitors.
Substitute Jarrod Bowen had a good chance in the second half to pull one back from Grosicki’s cross but blasted wide before Palace’s final flourish in the last five minutes.
Dawson brought down Jeffrey Schlupp for the penalty that Milivojevic converted and Van Aanholt scored from fellow substitute James McArthur’s through ball.
(Reporting by Rex Gowar; Editing by Toby Davis)
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