The Dons were coasting by half-time thanks to Niall McGinn's free-kick and a close-range strike from Calvin Zola, and added a third thanks to Michael Hector's wonder-strike, before the defender turned provider as McGinn tied things up with four minutes left.
They had to reshuffle their side with full-backs Joe Shaughnessy and Clark Robertson out. Shaughnessy was suspended after his red card on League Cup duty last week, while Robertson is set to undergo surgery on a knee problem.
Their places in the starting XI were taken by Andrew Considine and Cammy Smith, while Hector replaced the rested Russell Anderson.
Alan Archibald's Thistle side could have leapfroged managerless Hibernian with a win, but were without defender Conrad Balatoni. Former Barcelona defender Gabriel Piccolo stepped into a side otherwise unchanged from the 2-1 defeat to Celtic last week.
Both sides were keen to play the game in an entertaining manner, but the clash was beyond the quarter hour before either goalkeeper was really tested.
Johnny Hayes put in the cross from the right and it was met by Zola, but Scott Fox in the Thistle goal showed why he has been drafted into the Scotland squad, diving to his right to turn the striker's volley away.
But Fox was beaten after 25 minutes. Aberdeen-born Aaron Taylor-Sinclair brought down Hayes 25 yards from goal in the right-hand channel, and McGinn stepped up to curl round the wall and inside the goalkeeper's left-hand post.
The Dons were 2-0 up 14 minutes later. Peter Pawlett, who had been lively for Derek McInnes' side, weaved his way to the by-line, and sent a low ball across the face of goal, which Zola slid over the line from close range.
There was a flashpoint just before the break as Thistle's Kallum Higginbotham reacted to a strong Ryan Jack challenge, the former Huddersfield man picking up a yellow card for his trouble.
Thistle were playing some neat stuff in their approach play but were struggling to test Jamie Langfield in the Aberdeen goal.
When James Craigen shuffled onto his left foot 20 yards out, his rising shot wide of the upright was the closest the Jags had come.
The Dons had already brought on Barry Robson for Smith, and Scott Vernon replaced goalscorer Zola after 63 minutes.
The second substitute had been on the park just seconds when the Dons added a third, but it came from an unlikely source.
Thistle half-cleared a free-kick, and the ball dropped to on-loan Reading man Hector, who thundered a stunning 25-yard effort into the top corner of the net.
It was a quality goal, but Hector's strike was almost outdone just seconds later. Straight from the kick-off, Higginbotham spotted Langfield off his line and sent an audacious lob over the goalkeeper, only to be denied by the crossbar.
That sparked the Jags into life, and over the next five minutes, Higginbotham would twice be denied by Langfield, the second effort taking a big deflection and almost looping into the net.
The Jags were enjoying their best spell but the introduction of Ross Forbes and Christie Elliot for Kris Doolan and Craigen after 69 minutes seemed to disrupt their flow.
Ten minutes later, both sides made their final changes, Anderson replacing Pawlett for the Dons, while John Baird took the place of Higginbotham.
McGinn put the icing on the cake four minutes from time, when he raced in at the near post to volley home Hector's right-wing cross and seal a superb win.