Martin Paterson pounced on indecision in the Hull defence to score the only goal of the game and secure Burnley's sixth win in seven Championship games.
Jack Hobbs and goalkeeper Peter Gulacsi left a clearance to each other as the striker showed no such hesistation.
Hobbs could have scored at the other end before the opener while Robert Koren came closest to an equaliser for the Tigers after the break.
Victory moves Burnley up to seventh, three points behind sixth-placed Hull.
The Clarets had the ball in the net before Paterson's opener as top-scorer Jay Rodriguez stabbed home only for David Edgar's flick-on to be judged to have come from an offside position.
But the visitors enjoyed the best of the opening stages with Hobbs drilling wide from 12 yards and Aaron McLean fizzing a shot across the face of Lee Grant's goal before their side fell behind.
Koren was the chief culprit in Hull's profligacy, missing the best of the chances to pull level.
The Solvenian playmaker slashed wide when picked out by Andy Dawson in the second half before blazing over from McLean's cross.
Rodriguez could have made the points safe but spurned a clear opening and the home fans nerves were frayed as David Edgar's header almost sneaked past team-mate Grant in his own goal.