The Terriers, who took all the spoils at Turf Moor for the first time in 41 years, had scored just once in the previous four league fixtures but Vaughan produced a predatory finish with their first real chance of note 10 minutes after the interval.
It was winger Keith Treacy, who was the first to test Alex Smithies in the Terriers goal with a swerving effort which the shot-stopper just managed to prevent squirming underneath him.
Dane Richards' pace then proved to be personal hazard when Smithies wiped out the Clarets substitute in the act of rescuing Paul Dixon's poor header back towards goal.
Both players carried on but Oscar Gobern sustained a head injury shortly afterwards and he was unable to continue so Scott Arfield, initially dropped to the bench by Robins, entered the fray.
Burnley began to up the ante with Danny Ings' cross narrowly evading Charlie Austin's near-post run before the ex-Bournemouth forward sliced a great chance wide after Treacy's effort deflected into his path.
The hosts did look the more likely to break the deadlock as they sought to breach a defence which had conceded 19 goals in their last four league trips.
That breakthrough almost came less than five minutes after the break when Antony Gerrard's costly slip saw Austin set free. The striker appeared caught in two minds, though, and it was difficult to tell if his delicate chip which went wide was intended for the goal or the flying Richards at the back post.
However, the visitors, who had yet to threaten Lee Camp's goal took a shock lead in the 55th minute courtesy of on-loan Norwich striker Vaughan.
Sean Scannell's cross came out to Adam Clayton and he planted a left-foot shot at Camp, who just looped the ball in the air where the alert Vaughan was on hand to stab home.
Sean Dyche's response was instant as he hauled off substitute Richards for another striker in the shape of Sam Vokes, while Marvin Bartley replaced Chris McCann minutes later.
And the changes almost paid dividends as Bartley bent a beautiful ball in to Vokes, who flashed his header against the crossbar.
At the other end, Theo Robinson, making his first start since returning to Huddersfield on loan, could have wrapped it up had he not shot tamely at Camp.
Robins' men survived a double scare when Treacy and Ings both went close, Smithies make a fine stop from the latter at the death, as they held on to take a vital three points back across the Pennines.