The first chance of the game fell to Patrick Cregg, whose shot was tipped over the bar by Paul Gallacher in the Thistle goal.
Just moments later, May found space in the Jags area and slotted his effort past Gallacher to give the Saints the lead at Firhill Stadium.
The hosts looked to reply through Kallum Higginbotham's curling strike on the half-hour mark, though the ball failed to trouble Steve Banks. Loanee Chris Erksine also came close to levelling the contest, but fired his chance just over the bar.
Alan Archibald's side started the second half well, as they worked a corner well for Lyle Taylor to get a shot in at goal which sailed narrowly over.
Thistle continued to attack, though failed to take any of their chances, and remain one place above the drop zone.