More than 2,000 Thistle fans made the trip with their side needing only a point for promotion, but they were almost silenced just four minutes into the game when Conor McGrandles forced Scott Fox into a save.
Alan Archibald's men soon gained a foothold in the game, however, and should have opened the scoring in the 31st minute when Conrad Balatoni headed wide from close range.
Ross Forbes then struck the crossbar with a left-footed free-kick two minutes later as the Jags continued to threaten.
The visitors found the goal they were looking for five minutes into the second half when Andy Dowie headed home Forbes' corner.
Chris Erskine ensured the celebrations could really start with a clinical 78th-minute finish.