Kamara ran in behind the Hull defence early on but his shot from six yards was easily collected by Boaz Myhill.
Moments later the ball fell to Kevin Phillips in the box with acres of space to get his shot away, but his finish was lacking as he sent the ball wide of the post from 10 yards.
Jon Parkin tried his luck for Hull midway through the half but his right-footed effort from the edge of the box trickled wide of the post.
Nicky Forster then came close to open the scoring for the home side as he fired in a right-footed shot from the edge of the box forcing Dean Kiely to stretch and turn the ball around the outside of the post.
Jason Koumas came within inches of putting the visitors ahead just before the break as he struck a right-footed shot from the edge of the area and it smacked against the post with the Hull defence clearing the danger.
Kamara tried his luck early in the second half, but his shot from the edge of the box was comfortably saved my Myhill.
Kamara did score however on 61 minutes as Koumas ran at the Hull defence and slipped a neat ball through to the Albion frontman who blasted the ball past Myhill from ten yards to put his side ahead.
Hull then had keeper Myhill to thank as he first made a save from a close-range Nathan Ellington header and then, from the rebound, Ellington fired a shot at Myhill which he palmed away.
The ball then fell to Richard Chaplow who curled in a right-footed shot from 20 yards which the Hull man managed to tip over the bar.
Ellington came close late on but his left-footed shot from 15 yards flew into the side-netting.