On Alex Smith's return to the Falkirk dug-out they handed the veteran gaffer his fifth win at the club in seven attempts in a victory that should lift
The win lifts the Bairns above Inverness in the league table, but only as far as eighth in the Ladbrokes SPFL Championship.
Falkirk spent the first half playing on the counter attack but they had the best chances too.
David Mitchell in the Bairns' goal was a safe and assured presence and held anything Morton threw at him, while Derek Gaston was tested several times by the Bairns.
Alex Harris sent a dipping strike just over early on, Austin fired straight at Gaston then O'Hara curled the rebound just wide and the Morton number one had to push over a fizzing Aaron Muirhead effort from 30-yards.
Mitchell did have to make a smart stop in the first half, down low to stop a Ross Forbes effort and another from the same player sailed over right on the stroke of half-time.
The Bairns were not exactly settled, after a week of big changes at the club, but they were holding their own at Cappielow. That changed in the second half where they improved and saw out the win.
Goalkeeper Mitchell was one of four changes made by Alex Smith and took his chance between the sticks in an assured display.
Smith last took to the dugout at Cappielow during the interim period between Steven Pressley and Gary Holt's management of the Bairns, and handed Will Vaulks a debut here in Greenock. That game ended in a 2-0 defeat for the Bairns but today was a success.
The changes made this time around - some three and a half years later and with Lee Miller and Michael McArdle beside him and Mark Kerr on the park - were not as notable, but a return to winning ways was the big switch in Falkirk's season.
Harris came close again to a breakthrough straight from the restart but that elusive win seemed so close, yet so far for the Bairns who were well matched by Morton.
It all swung on the 62nd minute and from an ex-Morton man Joe McKee. Just as he did at Dundee United in last season's promotion play-off he caught the majority of the ground unawares with a set-piece. He rattled a low drive into the corner from 30 yards to send the Bairns ahead.
The Bairns should have doubled their lead through sub Lee Miller who headed a great chance wide.
With something to hang onto the Bairns suddenly seemed more assured, aided by Mitchell at the back. Seeing the games through is something that was lacking under Peter Houston with nerves often creeping in - even when Falkirk were ahead.
Not this time. They continued to battle. Tom Taiwo took a sore one tackling Robert Thomson and was soon replaced by Cameron Blues as the Bairns looked to see the game out, and they managed it, for the sixth time this season, and for Alex Smith's fifth win as Bairns boss.