Alan Campbell's 36th-minute opener set the home side on their way before Terry Masson doubled their lead shortly after the interval.
Garry Wood struck Montrose's third before Ross McCord was dismissed for two bookable offences and Max Wright pulled one back for East Stirling with seven minutes remaining.
However, the hosts restored their three-goal advantage in stoppage time as Wood scored his second of the afternoon from the penalty spot.
Allan Moore won his opening league match as Arbroath manager as they came from behind to seal a 2-1 victory at Berwick Rangers. A blunder from Arbroath goalkeeper David Crawford handed Berwick an opening goal after eight minutes as Paul Willis pounced to score. However, shortly after the break the visitors equalised when Berwick goalkeeper William Bald parried the ball into Kevin Buchan's path and the substitute made no mistake.
Seven minutes later the Arbroath turnaround was complete as Paul McManus struck a stunning free-kick beyond Bald via the crossbar.
Also making a winning league start was Albion Rovers player-manager Darren Young as his side earned a 2-1 success against Annan Athletic at Cliftonhill.
After Steven Logan was fouled, David Hopkirk fired Annan into the lead with a penalty in the 30th minute. The game was transformed after half-time as Alan Reid's cross was volleyed home by Gary Phillips to restore parity for the Coatbridge hosts. Two minutes later, Rovers netted what proved to be the winner as Michael Dunlop headed home.
Barry Ferguson's Clyde went a goal down before winning 2-1 at Queen's Park.
The hosts' Darren Miller was a constant threat in the opening period and his 19th minute free-kick forced Clyde's Jamie Barclay into an excellent save.
Miller then got the better of Barclay in the 59th minute as he scored directly from a corner-kick to hand Queen's Park the lead. However, Anthony Quinn's foul on Scott Ferguson gifted Clyde a 78th minute penalty which was converted by Ross McKinnon and with less than two minutes remaining, striker Michael Daly pounced from close range to score Clyde's winner.
Barry Wilson's Elgin City rode their luck to snatch a 1-0 win over East Fife at Borough Briggs.
The visitors almost opened the scoring on the half-hour mark when Jon McShane's free-kick was smartly saved by Elgin goalkeeper Michael Fraser.
Fraser then misjudged a cross in the 70th minute, but East Fife's Nathan Austin headed wide and it proved a costly miss as a minute later Craig Gunn reacted sharply to drive home Elgin's winner.