Kris Doolan had put the hosts a goal to the good at half-time in the cross-Glasgow clash.
But Callum Ball's introduction in the second half added an extra dimension to the Saints' attack - the former Derby County man netting on the hour mark after a fine cross from Jeroen Tesselaar.
And McLean kept his nerve in the fifth minute of stoppage time to convert the penalty after Abdul Osman handballed.
Poor defending from Tony Craig's men saw Partick dominate much of the opening stages and an unmarked Doolan headed them in front from Steven Lawless' cross 22 minutes in.
James Marwood and McLean both passed up opportunies to equalise in the first half, but Partick went in ahead and looked well-set for their third win of the campaign.
However, Ball's introduction in the 53rd minute added physicality to the Saints' side and sent panic through the home defence.
And Ball was the man to get Saints level, steering in Tesselaar's accurate centre.
The 21-year-old almost snatched a winner after neat footwork in the area, but Osman handed captain McLean the chance to take the points even later and the midfielder duly delivered.
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