Andrew Gray's first-half double condemned Huddersfield Town to a second successive Championship defeat and earned a fourth win in five games for Burnley.
A late own goal by centre-back Michael Duff rewarded a spell of Town pressure, but those two goals by the Clarets' £9m signing from
Brentford, the first a penalty, proved too big a hurdle to overcome.
Town boss Chris Powell made two changes, leaving club-record signing Nahki Wells on the bench as on-loan Jamie Paterson and Muzzy Carayol came in.
It was only a second start for Nottingham Forest forward Paterson, while Middlesbrough winger Carayol came in for hamstring injury victim Sean Scannell.
Burnley were unchanged as they looked to build in their derby win at Blackburn Rovers and maintain their push for an immediate return to the Premier League.
Town started well, with Harry Bunn having a shot deflected for a corner, but were trailing after 12 minutes following Joel Lynch's foul on Gray, who put away the spot kick.
Sam Vokes had a shot held by Town keeper Joe Steer while it took a timely tackle by skipper Mark Hudson to thwart Town old boy Scott Arfield.
Steer made another good save, this time from George Boyd, before town forced a string of corners, but were unable to find a way through.
Burnley doubled their advantage two minutes before the break, when Vokes passed to Gray, who held off Hudson to drill home low with real pace and power.
Town's Ishmael Miller shot wide on the turn early in the second half, but Burnley were soon back on the front foot, and Vokes had a shot saved before Michael Keane headed just over.
Dean Whitehead got a 58th-minute booking for a foul on Gray which means he will be suspended for Tuesday's game at Reading after picking up five for the season.
Town replaced Miller with Wells, then Carayol with Dempsey, and Wells hooked one over before having a shot saved by Tom Heaton, who then parried a well-struck effort by Emyr Huws.
The home defence was finally breached when Duff could only put a Dempsey cross over his own line, and Burnley had a big escape when Bunn then shot over when well placed.
