The home side started strongly and could have taken the lead inside the opening 10 minutes but Chris McCann could only poke Kieran Trippier's pinpoint cross wide of the target.
Burnley were dominating possession and Keith Treacy almost broke the deadlock as he beat the Calum Woods before firing at goal but Alex Smithies was on hand to make a good save.
Danny Ings had a great chance just before the break as he reacted first to Treacy's deflected shot but he could only fire wide from inside the penalty area.
After the break the Terriers came out strongly and took the lead through Vaughan as tapped in from close range after Lee Grant could only parry Wood's initial effort.
The Clarets responded as Marvin Bartley got the better of Adam Clayton before crossing into the area where his cross was met by Sam Vokes, but his header clattered off the bar and was cleared.
Huddersfield had a great chance to finish the game as Sean Scannell released Theo Robinson, who skinned two defenders, before firing at goal but his shot went just wide but the Terriers secured three vital points.