Despite the setback of conceding an early goal the Bairns rallied back to finish the game as commanding winners as the League 2 side ran out of steam by the second half.
Rovers took the lead after the Bairns failed to clear a free kick into the area on 12 minutes and it eventually came to Charlie Reilly at the back post who dragged it back to the centre from the touch line for Max Wright to score into an open net.
The goal seemed to wake Falkirk up and they began causing Rovers problems in the final third with the defence having to deal with through balls and crosses but a switch from left to right was picked off by Charlie Reilly 20 minutes who went box to box and forced Mutch in to a decent block to stop the visitors going 2-0 up.
The Bairns were then level on 23 minutes and it was Callumn Morrison, last season's top scorer, with the first goal of the season.
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The winger got in behind the defence and a good bit of skill took it away from Alfie Robinson before curling it past Cammy Binnie and in to the top left corner for the equaliser.
Morrison made it 2-1 on 29 minutes when Jamie Wilson controlled a Seb Ross cross in the box and played it to the winger at the angle who once again cut inside and curled it around Binnie and in to the far corner.
35 minutes Morrison turned provider when he whipped a corner in from the right and Paul Dixon made a run to the front post to head it back across goal and in to the far corner.
Morrison continued to terrorise the Rovers defence after the break and was brought down in the box on 58 minutes.
He stepped up to take the penalty himself but Binnie was equal to it and parried it away from his right hand corner.
Charlie Telfer made it 4-1 on 84 minutes when he rifled a shot in off the underside of the bar from 20 yards and substitute Ben Weeks opened his account for the season one minute later with a neat finish inside the area to cap off a good team performance.