Hull created a chance early on when Paul McShane floated in a right-footed cross, but Daniel Cousin couldn't get enough power on his header as his effort from five yards was comfortably saved by Robert Green.
Carlton Cole then missed a great opportunity for the visitors when Craig Bellamy raced down the left and played in a neat ball into the feet of the striker, but the ex-Chelsea man could only place the ball straight into the arms of keeper Boaz Myhill.
Hull created a chance midway through the half when Marlon King swung in a cross from the left which Dean Marney met with a thumping volley at the back post, but his effort flew wide of the left-hand post.
Marney then tried his luck again, this time from 25 yards but his right-footed strike flew just over the crossbar.
Herita Ilunga had a clear chance to put his side ahead on the half-hour mark when Matthew Etheringon picked him out in space from a corner, but the Hammers full-back could only glance his header well wide.
The home side took the lead on 51 minutes when Turner rose to thump in an Andy Dawson corner from six yards out with a pin-point header.
Gianfranco Zola's men nearly equalised within seconds when Valon Behrami played a neat ball into the feet of Cole who managed to turn his man and fire in a right-footed shot from close range, but the ball slammed against the crossbar allowing the Hull defence to clear.
Kamil Zayatte then tried his luck from distance for the Tigers but his 25-yard effort whistled just over Green's crossbar.
Phil Brown's men continued to battle and closed out all West Ham could throw at them to complete a well-earned win.