The Dons are now seven points behind the reigning champions, who have played one game less than the challengers.
A frustrating afternoon for the home side started well enough, when teenager Lawrence Shankland, who was making his first start for Aberdeen, sent a snap-shot just over the bar with two minutes on the clock after good play from Jonny Hayes.
At the other end of the pitch, Steven Lawless fired just over following a swift counter-attack from the visitors, with Ryan Stevenson at the heart of the move.
Shankland went close again when the Aberdeen forward sent a header over the target, this time from a superb Ryan Jack delivery.
Thistle were forced to bring on Lyle Taylor for the injured Kris Doolan and the striker strode through the heart of the Aberdeen defence only to be denied by the advancing Jamie Langfield.
Taylor then squandered another chance when he went clean through on goal again, and this time he fluffed an attempted chip over goalkeeper Langfield to send the ball wide of the post.
In the opening minute of the second half, James Craigen used his pace to leave Andrew Considine flat-footed and his powerful drive was tipped over the bar by Langfield.
Thistle continued to have the better of the play without creating any clear-cut opportunities against an out-of-sorts Aberdeen.
The visitors did survive a scare eight minutes from time when referee Kevin Clancy pulled play back when Hayes burst through on goal, but the Dons winger was adjudged to have won the ball with a high boot.