Kris Doolan had given Partick a 22nd-minute lead, but substitute Callum Ball levelled things up on the hour and McLean dramatically completed the comeback.
The visitors to Firhill Stadium had lost all five of their previous games and were quickly on the back foot as John McGinn and Ryan Stevenson shot wide during early pressure from the home side.
Doolan gave Thistle a deserved advantage when St Mirren defender Eli Plummer allowed him to get free in the box to head home after good work from Steven Lawless on the left flank.
A feisty next 35 minutes saw four yellow cards handed out, but no addition made to the scores, and the game began to swing St Mirren's way following the introduction of Ball off the bench.
The striker prodded in his first Buddies goal from Jereon Tesselaar's cross to the back post on 60 minutes.
Thistle midfielder Abdul Osman had arguably been the best player on the pitch prior to handling in his own box deep into stoppage time, and McLean kept his cool from the spot to end St Mirren's sorry start to the campaign.