The visitors, just three points above the Championship drop zone coming into this clash, hit the ground running and took the lead after just two minutes thanks to the Norwich loan striker.
The 24-year-old then scored two simple headers to make it 13 for the season and he could have netted two more, had Bristol City keeper Tom Heaton not made two top-drawer saves.
In their final home match before relegation to the third tier City grabbed a last-gasp consolation through Lewin Nyatanga.
The pre-match talk surrounded the absence of in-form striker Jermaine Beckford, but Vaughan stepped up to the plate in the perfect fashion, slamming Lee Novak's cross home for his 11th of the campaign.
Huddersfield had not won successive matches since October but they looked set to break that unwanted run in the 13th minute when Vaughan grabbed his second of the afternoon and his third in two games.
The striker rose unmarked to nod home Oliver Norwood's free-kick from the left flank five yards out to delight the 1,546 travelling fans and to give Mark Robins' men some breathing space.
And just seven minutes later the former Everton man was denied a 17-minute hat-trick by a superb Heaton save after the striker was sent through by Novak's clever pass.
After a scrappy start to the second half O'Driscoll introduced former Huddersfield striker Jon Stead, back to full fitness after a spell on the sidelines, for Marvin Elliott as his side looked to score their first goal since April 16.
Albert Adomah, City's man of the match in the 0-0 draw with Hull last weekend, almost gifted Novak the ball on the hour mark when his back pass to Heaton went wrong.
But Huddersfield only had to wait three minutes for another goal, Novak crossing from the right wing for Vaughan to complete his hat-trick with a simple header from close range to wrap up the points.
At the other end Novak and Vaughan linked up once more, but Heaton denied the latter with a smart stop.
Adomah has been linked with a move away from Ashton Gate in the summer and he had the game's next chance but he headed wide from six yards out in the centre of the penalty area.
And they did grab a consolation in the 90th minute, Wales defender Nyatanga heading in at the far post.