Neither Partick nor Morton had enough guile to find the net at Firhill despite a host of chances being created on a battle-scarred pitch.
The slackness in front of goal was best summed up just before the hour mark when the visiting Archie Campbell ballooned a second-half penalty into the stand housing the travelling Greenock fans.
Thistle dominated the first half, but visiting shot- stopper Colin Stewart denied Kris Doolan with a fine one-handed save before turning round a shot from the same striker after he outfoxed Morton’s offside trap.
As Thistle kept on the offensive, Morton youngster Thomas O’Ware was inches away from turning a curling Doolan shot into his own goal.
Nine minutes into the second half, Thistle’s Paul Cairney released Chris Erskine who crossed for Doolan to tap home, but he was offside.
Morton were then given an opportunity to sucker punch their hosts when Stephen O’Donnell brought Peter MacDonald down in the box. Campbell took the spot-kick, but fired his effort high over Scott Fox’s goal.
Campbell had no better luck 17 minutes from time when Fox beat away his effort, with the follow up from substitute Darren McGeough being deflected into the side-netting.