Huddersfield Town 1, Burnley 3
Burnley went ahead after 12 minutes when Michael Keane headed on David Jones' corner, and Stephen Ward hooked the ball beyond Jed Steer for his second of the season.
And on the half hour it was 2-0 as Andre Gray held the ball up superbly before playing in George Boyd, who advanced and picked up Sam Vokes to claim his 13th of the campaign at the near post.
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Hide AdRight on half-time Town got a lifeline out of nothing as Joe Lolley picked the ball up on the right, cut inside former Terrier Scott Arfield and curled a shot inside the far post.
But the Clarets deservedly restored their two-goal lead in injury time as Ben Mee thumped a header inside the top corner from another Jones corner.
Town responded well after the break, and Jason Davidson hit the angle with a volley from substitute Jamie Paterson's raking pass, but Arfield was denied a fourth goal for Burnley when Mark Hudson made a big block as the midfielder looked set to pick his spot from Jones' pass.
The Clarets didn't need another goal, however, as they comfortably saw the game out for another three points.