Burnley had a chance early on as the ball dropped nicely at Andy Gray's right shoulder just outside the area, but he couldn't make his half-volley count as it bounced wide of Boaz Myhill's right-hand post.
Minutes later Burnley had another chance through Graham Branch who found himself in space on the left channel and sent a half-volley from just inside the area which zinged past Myhill's left-hand post.
Ryan France had a chance for Hull midway through the first half but his right-footed volley inside the area was neatly saved by Burnley keeper Brian Jensen.
Burnley should have scored soon after as Branch powered into the left side of the box and played the ball across the area for an easy tap in but Leon Cort raced back to clear the danger for a corner.
Jon Parkin found himself with a chance towards the end of the half after neat play created a chance for him on the edge of the area but Jensen comfortably saved his left-footed volley.
Hull had the last chance of the half as the ball fell to Kevin Ellison on the edge of the area but he fired his half-volley just over the bar.
Alan Mahon came close for Burnley early in the second half as his left-footed shot flew over the bar from 12 yards.
Burnley nearly went ahead midway through the half as Kyle Lafferty found himself clear in front of goal but his shot from inside the six-yard box was saved well by Myhill as he stood his ground and deflected the ball wide for a corner.
Mahon came close again for Burnley minutes later as his curling free-kick from the edge of the box went inches wide of Myhill's left-hand post.