A header from Michael Turner and a Phil Neville own goal saw the Tigers comfortably in front, but second-half strikes from Tim Cahill and Leon Osman drew the game level.
The home side came close to taking the lead early on as Peter Halmosi raced down the left and swung in a cross towards Bernard Mendy, but the Frenchman's header was well saved by Tim Howard.
Everton had a chance soon after as Neville played the ball into Osman, who found space in the box but he could only drag his shot wide from 12 yards.
Hull then took the lead on 18 minutes as Dean Marney swung in a right-footed corner onto the head of Turner, who made no mistake at the back post with a thumping finish.
Yakubu had a chance to level soon after but his half-volley from just inside the box was well turned away by keeper Boaz Myhill.
A foul by Neville on Halmosi midway through the half saw the Tigers awarded a free-kick on the edge of the box, but Marlon King's rifling effort sailed past the post.
Phil Brown's men found themselves 2-0 up early in the second half as another curling corner from Marney caused confusion in the Everton six-yard box resulting in Neville heading the ball towards his own goal past a flailing Howard and into the back of the net.
Substitute Louis Saha had a great chance to grab one back on 60 minutes as he raced 20 yards in on goal, but his effort from 12 yards was saved tremendously by Myhill.
The visitors did grab one back on 73 minutes as the linesman ruled Cahill's effort had gone over the line as he smashed the ball against the underside of the crossbar from 10 yards.
Everton took the game to Hull and drew level on 78 minutes as neat work from Saha allowed Yakubu to play in a low cross from the left to Osman, who fired the ball into the back of the net from eight yards.
Osman nearly found the winner in the dying minutes but his arrowed effort from 20 yards whistled just over the bar.