Alan Archibald's side dominated large swathes of the match but their inability to take chances was again their downfall.
St Mirren, who had the satisfaction of retaining their one-point advantage over their hosts, needed a penalty near the end of the first half to cancel out Kris Doolan's earlier strike. But although the scorer, Kenny McLean, later hit the post, his side could not justifiably claim they had done enough to entirely pull away from the trouble zone.
"I thought we did enough to nick the game and be able to relax tomorrow, but we'll take the positive of a point," said Archibald. "I thought it was a very soft penalty. I've seen them given, and not given, so it's just your luck."
Danny Lennon, the visiting manager, said: "Once again I've got to praise the character of my players. It wasn't a game for the purists tonight but it was also a fantastic atmosphere and an emotional occasion. Every point we pick up now is so important. That's another part of the race [to escape the play-offs] finished and we're in the lead at the moment."
Lennon's side scored in only 13 seconds against Hibernian last Saturday, and on a wet, murky evening in the north of Glasgow it did not take them much longer to threaten Paul Gallacher's goal. Thistle failed to clear an attack but John McGinn's weak shot provided a reprieve for the hosts. What was to prove a highly misleading start to the half continued when Jason Naismith's goal-bound shot was blocked by Jordan McMillan, but after dominating the first five minutes the visitors did not show up again until the last five.
Instead, and inspired by Kallum Higgenbotham, Thistle took a total grip on the game, not allowing any space and forcing St Mirren to give the ball away carelessly. Chris Esrskine and Aaron Sinclair-Taylor, from a free kick which Conrad Balatoni could not quite get a touch on, provided moments of danger for Chris Dilo before Higgenbotham's inspired play gave his side the lead.
The game had gone through a scrappy phase, being interrupted for numerous free kicks, when Higgenbotham, oozing confidence, lifted it above its mediocrity.
Switching to the left he bamboozled the visiting defence but James Craigen could not quite get enough purchase on his team-mate's cross.
Sixty seconds later there was an action replay and this time when Higgenbotham's delivery reached the far post it was headed past Dilo by Doolan for his 10th of the season.
The visitors, who had beaten Hibs comfortably with only 10 men, had captain Jim Goodwin batting for them after appealing his red card, but continued to look a poor second.
They could have been punished further had Doolan got the touch required to deflect Taylor-Sinclair's low shot into the net but instead lost their lead in circumstances which displeased the home supporters.
Just as they had started the half vigorously, St Mirren woke up near the end of it with Lee Mair causing Thistle palpitations when he sclaffed the ball over his own bar. Goodwin had a shot cleared by Balatoni and then, from a corner, Naismith crumpled in the box under a challenge from Higgenbotham.
Referee Calum Murray, who minutes earlier had received an earful from Stephen Thompson after waving away a penalty claim, immediately pointed to the spot. Kenny McLean stepped up and, with jeers ringing out from the Thistle fans, calmly placed the ball low inside Gallacher's right hand post.
Even with the interval arriving to allow them to recover their composure, Thistle took some time to regain it when they reappeared for the second half with Gary Fraser on for Prince Buaben. When they did get back into their first-half stride, on the hour, it was inevitably Higgenbotham who set up two great chances.
Back on the right, his free kick found Mair but the defender's diving header bounced over the bar. Higgenbotham's next delivery was a low, hard cross, but again it just evaded substitute Christie Elliott.
With the deteriorating conditions adding to the cup tie atmosphere the visitors then had two quick chances themselves to take the lead. McLean curled a terrific low shot from 20 yards which hit the base of the far post and rebounded to safety and then, from further out but a similar angle, left-back Sean Kelly's shot was deflected past the same post for a corner.
Thistle had the best of the final exchanges and came closest to getting the win their performance deserved when substitute Lyle Taylor met Fraser's cross - but he saw his looping header hit the bar on a night of missed chances for his side.