The visitors were the first team to threaten as they won a corner and Curtis Davies beat his marker to the ball and headed just wide of the target.
However, Everton were soon on top as Romelu Lukaku forced a good save from Allan McGregor, but from the resulting corner Kevin Mirallas gave the home side the lead as he side-footed the ball into the bottom corner, beating an unsighted McGregor, who failed to move for the ball.
The Tigers came close to getting an equaliser through Abdoulaye Faye as he had two attempts from inside the box with headed efforts, but could not hit the target.
However, Steve Bruce's side were level when Yannick Sagbo converted from close range with an emphatic finish after Sone Aluko had done well to beat Gareth Barry down the right and found his teammate with a pinpoint cross into the area.
Hull should have been ahead jut before half time when Faye again met a corner from Robbie Brady and his header was directed into the path of Aluko, who nodded it at goal, but Leighton Baines was on the line to clear.