The home side found themselves 3-0 up at half-time thanks to goals from Stephen Hunt, Andy Dawson and Dean Marney.
However, the Tigers made it difficult for themselves in the second half after Kamil Zayatte first scored a freak own goal then conceded a penalty, which Louis Saha coolly converted, the visitors were unable to grab an equaliser; leaving them one place above Hull in 14th.
Hull opened the scoring on nine minutes as a deflected cross from Hunt on the left landed at the feet of Jozy Altidore, whose effort from close range was parried by keeper Tim Howard but only into the path of Hunt, who fired the ball into the top left corner of the net to register his third goal of the season.
Geovanni tried his luck minutes later but his arrowed right footed effort was comfortably saved by Howard.
- Hull City 3-2 Everton: As it happened
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Phil Browns men were 2-0 up on 20 minutes as a Joseph Yobo foul on Geovanni allowed left-back Dawson to step up on the edge of the area and send his left-footed free-kick curling into the top right corner of the net to bag his first goal of the campaign.
Marney then made it 3-0 to the Tigers on 28 minutes as the Everton defence failed to clear a cross from Hunt , allowing the ex-Tottenham midfielder to nip in and send a deflected shot into the bottom right corner of the net from 12 yards.
Leighton Baines tried his luck for the visitors early in the second half but his run and shot from 20 yards was well saved by keeper Matt Duke.
Everton grabbed one back on 49 minutes as a cross from Johnny Heitinga was turned into the back of his own net by Zayatte, whose attempted clearance looped over Duke to make it 3-1.
The Toffees were then awarded a penalty on 64 minutes as Zayatte was adjudged to have brought down Saha inside the area. The ex-Manchester United man took the spot-kick himself and sent Duke the wrong way to put his Everton side firmly back into the game.
Richard Garcia nearly extended Hull's lead moments later but his speculative right-footed shot was well saved by Howard.