The away side made an encouraging start to the game with Sean Welsh forcing an early save from St Mirren goalkeeper Marian Kello.
James Marwood, who started in the absence of suspended player-coach and captain Jim Goodwin, had a chance for St Mirren before a low shot from Kenny McLean was saved by Scott Fox.
Jason Naismith fired over for the home side before McLean had an effort blocked in a far from eventful first half which St Mirren edged in terms of possession.
Partick started the second half the brighter of the two sides with Elliott heading wide before Gary Fraser had a shot which was well held by Kello.
Ryan Stevenson had a good opportunity to break the deadlock but his header on the hour mark failed to trouble Kello. Frederic Frans was the next to draw a save from Kello as the away side continued to apply pressure.
And they were rewarded for their attacking intent on 75 minutes when Declan McDaid found Elliot on the left side of the box who fired past Kello to put Thistle in front.
Marc McAusland went close with a header for St Mirren before Adam Drury rattled the crossbar in added time, but the home side remain 11th in the Premiership, ahead of Ross County on goal difference.