The Yorkshire club started brightly and came close to opening the scoring when James Vaughan twice produce good saves from Clarets keeper Tom Heaton.
Martin Paterson almost broke the deadlock midway through the first half, but saw his diving header come back off the woodwork with Heaton beaten.
Vaughan blew an excellent chance to score when he sent his shot well over the bar from close range 10 minutes before the break.
They did take the lead five minutes after the restart thanks to Oliver Norwood's right-footed shot.
The Terriers were given a penalty moments later when Michael Duff was adjudged to have handled the ball in the area, although replays suggest that the incident took place outside the box.
Despite protests from Sean Dyche and the Burnley bench, Vaughan converted the spot kick to double the hosts' advantage.
The game became feistier after the penalty decision and referee Eddie Ilderton was called in break up scuffles between the two sets of players.
Burnley did manage to a pull a goal back six minutes from the end thanks to Danny Ings, but the Yorkshire side held on for a win that pulled them into the top half of the Championship, while Burnley saw their run of 12 games unbeaten come to an end.