Greg Kiltie, who has an enviable scoring record against the Bairns, fired Morton ahead just after half-time and Charlie Telfer made sure with the second after a defensive calamity between Ciaran McKenna and William Edjenguele laid it on a plate.
As far as afternoons go, this is as bad as Falkirk could have envisioned. Not only did they lose a vital three points, Partick Thistle leap-frogged them in the league table, and Queen of the South extended their advantage. And of course Morton.
AS IT HAPPENED: Matchday blog
Couple that with next week's opponents Dundee United maintaining a faint, forlorn hope of the title, and the Bairns' chances look slim. But not over.
The second half strikes, after a promising first half that lacked a little cutting edge, stunned the Stadium into silence. The discontented murmurs grew into boos shortly after the hour-mark.
Robby McCrorie kept Morton in it then, denying Aaron Jarvis and Zak Rudden with two improtant stops within a minute of each other. Rudden ran himself into the ground for the cause, but was doing it himself - winning possession, finding space and testing his Ibrox counterpart.
But it was Morton who passed the muster.
Falkirk made chances. Ross MacLean, one of a three-pronged attack, fed off a second ball from Jack Iredale but cut back rather than test Robby McCrorie and taps tamely for Morton to clear. Zak Rudden told him all about it, but it set the tone for the afternoon with the Bairns failing to pull the trigger, and Rudden, and Rudden alone, being forced to shoot from distance.
Morton threatened too but didn't test Harry Burgoyne with Kiltie and sub Andrew Dallas pulling efforts wide. The Wolves keeper did however have to push another Kiltie effort out with a key save that has been part of his repetoire since moving north in January.
Nikolay Todorov went close with a downward header inside the box that Rudden also failed to connect with, and the Bairns had a shout for a penalty. Zak Rudden beat Tidser to the ball, and hit the by-line. Gregor Buchanan slid in to tackle on the by-line and bundled the ball out for a corner but the South Stand appealled a hand was used.
Paul Paton was switched for Mark Waddington just before half-time but the roof fell in after the break. The Bairns were barked at during the interval, and went behind very shortly afterwards.
Greg Kiltie, a man who has form against the Bairns and holds an Indian sign over them with four of his 12 career goals coming against the club, opened the scoring from close range in the 47th minute after Charlie Telfer got beyond Ian McShane on the by-line and cut-back.
The Bairns looked shell-shocked and Morton seized the advantage and fired a second quickly afterwards.
This time it was their own undoing as Ciaran McKenna and William Edjenguele collided on the edge of the box, the Frenchman was laid flat-out and Morton had time to pick their spot in beating Harry Burgoyne, which Charlie Telfer did.
The Bairns simply had no answers.
Ray McKinnon rolled the dice with Aaron Jarvis and Tommy Robson pitched in for MacLean and Todorov but it says a lot when the biggest cheer of the home support in the second half came in repsonse to Robson's warm-up being stopped for his immediate introduction.
The changes did not bear fruit, though Jarvis and then Rudden forced Robby McCrorie into important stops a few minutes after the hour, and the on-loan Rangers goalkeeper denied his Ibrox colleague twice more when the Bairns star had to take it on himself.
In the end the Bairns were mocked by Morton after a season of bad blood between the sides. The home support turned on the club's board late on with a small band of fans staging a sit-in to direct chants at the club's senior management long after the final whistle.