Jordan Rhodes scored for the second successive game as Huddersfield picked up their first win on their return to the Championship.
Joel Lynch headed home a seventh-minute opener before Rhodes - who scored a late equaliser against Nottingham Forest on Tuesday - scored from inside the area just before the hour.
Ross Wallace had Burnley's best chance with a second-half free kick.
It was Huddersfield's first home win over Burnley for 56 years.
- Scored 40 goals in all competitions last season.
- Eight goals in eight appearances for Scotland Under 21s
- Grabbed a goal in his first start for the senior Scotland side in a 3-1 win against Australia on 15 August.
- Has two Championship goals from two appearances this season.
The home side were good value for the victory, although they took the lead in somewhat controversial circumstances.
Oliver Norwood's corner was headed in by Lynch but Burnley immediately remonstrated with the officials, adamant that Joseph Mills had cleared off the line. However, the goal stood.
Rhodes, who scored 40 goals in all competitions last season, twice went close after that, while Burnley had the ball in the back of the net on the stroke of half-time, only for David Edgar's effort to be ruled out for offside.
The three points were secured for Huddersfield, though, in the 58th minute when Rhodes rifled home from 12 yards with an effort that gave Burnley goalkeeper Lee Grant no chance.
Huddersfield boss Simon Grayson: "We aren't going to get carried away because we are only three games in. But we have come up against three established teams and done well.
"The players showed a positive attitude and the supporters back us.
"We never let them have two minutes on the ball and that is what you have to do against the top teams."
Burnley boss Eddie Howe: "For the majority of the game I thought we controlled possession, but in the final third we weren't ourselves and in both boxes I thought we were a bit of a disappointment.
"In the past two away games we've lost them both when we could have definitely picked up points in both.
"The reality is we haven't and we're disappointed in that, but I don't think we have been outplayed or outclassed. It's just a case of being a little bit better than we are and we'll endeavour to do that."
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