Fan favourite Lee Miller came off the bench to break a 90-minute deadlock at The Falkirk Stadium.
Morton had a late goal ruled out, when the ball crept over the line at a corner, but was chalked off by Euan Anderson, the referee.
The Bairns flew up the park and stole three points from a stalemate thanks to a moment of brilliance from striker Miller.
“We’re best when we move the ball quickly,” said Peter Houston, “and that was the move where we moved quickest and we got the goal. Otherwise we were lethargic in the second half.”
Morton made life difficult. Defeat is harsh on the Ton and remonstrations at full-time earned Thomas O’Ware a yellow card, but the Bairns fans were not complaining despite an awkward afternoon.
The Bairns were made to shoot into the south stand in the first half, for a change, after Morton won the toss and things really didn’t go the home side’s way from then on.
Morton packed the defensive third of the park and suffocated Falkirk’s first half attacks.
The Bairns were the attacking threat, but roisked being picked off on the break by Jim Duffy’s team, and both hit the woodwork.
First to do it was Ross Forbes with a rasping drive off the underside of the crossbar moments after he had curled a decent effort inches wide.
The closest Falkirk had come was the first minute header from Will Vaulks where he turend Craig Sibbald’s free-kick narrowly wide.
But the Bairns also went close through Blair Alston who poked against the outside of the post and Peter Grant hammered an Alston corner to the near-post into the side netting.
In the second half Peter Houston threw attackers David Smith and Lee Miller on, having already used a first-half sub to replace Tom Taiwo with Ryan Blair, but even the introiduction of fan favourite Miller and this season’s break-out star couldn’t swing the game out of the advancing stalemate it had become.
It was not an afternoon of drama, but nor was it a game for the faingt-hearted with several full-bodied challenges going in.
Danny Rogers was on the end of a clattering from Morton sub Alex Samuel after leaving his box to head clear - a challenge which earned the Morton man a booking.
There was a late chance for Smith which he knew little about, the ball ricchetting off the sub three yards from goal, but it trickled wide.
David McCracken almost scored the game-winner, but for Morton, with a headerwhich sent the ball back into the goalmouth from a corner and though Morton thought the ball had crossed the line, ref Euan Anderson ruled it out.
The game-winner came though after 90 and a half minutes and it was the fans favourite Lee Miller who stroked in the crucial blow for the Bairns.
The relief was clear with all outfield players piling ontop of the veteran in the corner of the park, and joined by the north-stand ball-boys.