Partick dominated most of this one but left mystified and frustrated that they did not claim all three points and remain in ninth positionin the Championship, with the Bairns one point ahead.
Thistle manager Gary Caldwell said: “I think if it had been a boxing match, someone would have thrown the towel in because we were totally dominant.
“Time will tell whether this was a missed opportunity or not because we knew it was a good chance to pull away.”
Scott McDonald had mixed fortunes. He was Thistle’s best player and scored an excellent goal but missed a great chance early in the second half.
He had given Thistle the lead on ten minutes, claiming his third strike in five games since reversing his decision to retire.
It was an excellent move as Blair Spittal drove the ball long down the right, where Lewis Mansell got away from William Edjenguele.
Mansell’s cross bounced up as McDonald went to meet it at the back post and he seemed to use his thigh to divert the ball past Harry Burgoyne off the underside of the bar.
James Penrice should have scored from a similar area in 24 minutes but lacked composure and shot over the bar.
Then Steven Saunders headed Craig Slater’s corner over in 35 minutes.
Inexplicably, Falkirk found an equaliser two minutes before half-time when Ian McShane shot home from close range after Deimantas Petravicius crossed from the left.
McShane then hit the post four minutes into the second half and McDonald headed Penrice’s cross wide from four yards out in 56 minutes.
Falkirk boss Ray McKinnon said: “A drew is probably fair but we feel we might have capitalised and got all three points.”