Thistle made a wonderful start to the match, scoring twice in the opening nine minutes through Kris Doolan and Conrad Balatoni before Stuart Bannigan sealed the win on 65 minutes.
St Johnstone arrived in Glasgow on the back of a victory over league leaders Celtic on their last visit to the city 10 days ago, but they were soon chasing the game at Firhill.
The home side struck on three minutes when Abdul Osman sent a cross into the box and Doolan rose above Steven Anderson to head the ball past Alan Mannus.
Thistle doubled the lead as Balatoni timed his run to the near post to get his head to a corner from Bannigan.
Mannus denied Partick a third goal a few minutes later as the Saints goalkeeper pushed a powerful drive from Ryan Stevenson over the bar.
Stevenson came even closer nine minutes before the interval when Murray Davidson headed the ball back into the penalty area and the Jags winger cracked his shot against the upright.
But St Johnstone squandered an opportunity to pull a goal back shortly before half-time when Michael O’Halloran got on the end of a Brian Easton cross and shot wide of the target with Scott Fox rooted to the spot.
Thistle started brightly in the opening stages of the second half as well and Balatoni nodded over from a Bannigan corner before Mannus comfortably dealt with Stevenson header from a long free-kick.
Scott was called into action on the hour when the Jags goalkeeper had to be alert to deal with Davidson’s header from another Easton delivery.
But Thistle secured the points five minutes later when Steven MacLean headed a free-kick from Stephen O’Donnell half clear and Bannigan smashed the ball into the next.
Partick were almost breached when the ball was slipped into MacLean but his shot was deflected behind the goal by Balatoni.