Vaughan scored the only goal of the game at Turf Moor in the 55th minutes in a game of few chances.
He told the club's official website: "It's given us a bit of breathing space, so we all want to kick on now and get as high up the table as possible.
"It was tough; a real grind. It wasn't the nicest game of football, but sometimes you have to play like that to get the three points."
Huddersfield are now 18th in the Championship following their victory and are six points clear of the drop zone with 12 games to play this season.