Saints looked to be heading for a pressure-relieving victory having edge ahead through Kenny McLean, but under-fire manager Danny Lennon saw the afternoon turn sour in the final 10 minutes.
The hosts were quickly into gear and came close to opening the scoring in the 11th minute - new loan signing Stephane Bahoken seeing his effort cleared off the line by Jags defender Conrad Balatoni.
Bahoken failed with two more attempts while at the other end, Partick saw appeals for a penalty turned down when Jim Goodwin barged over John Baird in the box.
Steven Lawless was an inch away from opening the scoring for Partick before the break - the midfielder's well-struck volley flashing just the wrong side of the post.
In the event, it was the home fans who were cheering soon after the break when substitute Gary Teale's cut-back was sweetly converted by McLean on the half-volley.
David Cornell then preserved the lead with a solid stop from James Craigen and McLean nearly converted more good work from Teale at the other end with the game opening up.
Cornell also denied Partick substitute Kris Doolan but just as it appeared Saints were edging their way to the points, Higginbotham curled home an excellent 81st-minute effort to silence home fans.
To rub salt in the wounds, moments later Doolan laid the ball back for Forbes to drill home a winner from 15 yards and condemn the struggling Saints to a fourth defeat in their last five games.