Morton thought they were on course to record a fifth successive Championship win and their first victory over the Bairns in 11 matches after substitute Lee Kilday netted in the 85th minute when he connected with Ross Forbes’ low near post free-kick.
But Lee Miller salvaged a point for Peter Houston’s side with literally the last touch of the game after heading in a Myles Hippolyte cross in the 93rd minute.
“I thought it would have been a travesty if we had not taken anything following our second-half performance,” said Bairns manager Houston, whose team remain fifth, a point adrift of Ton.
“Falkirk didn’t deserve to lose but when it happens in those dying seconds, it’s painful,” lamented Morton manager Jim Duffy.
“The guys are gutted in the dressing room and I am also gutted, but overall when you take a point away from here it is not the worst result in the world.”