John McGlynn’s side huffed and puffed and in the end didn’t have the creative spark to break down a well-drilled Angus outfit.
The offside flag saved the Bairns blushes early on when Craig Johnston fired home only to be flagged for his late run into the area.
Stewart Petrie’s side then forced the first save of the match with PJ Morrison collecting Graham Webster’s low shot.
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Falkirk’s first real chance came on 22 minutes, with Sean Mackie forcing goalkeeper Ross Sinclair into a smart stop after he was fed in by Ryan Williamson.
They should have gone in front on the half hour mark as they finally came into the game.
Brilliant work from Sean Mackie saw Callumn Morrison played in on goal, and his shot was then parried to Aidan Nesbitt who fired wide when it was easier to score.
In the second half, the 3,682 strong crowd were treated to much of the same with both sides failing to really take charge of the match.
Mark Whatley had the best chance of the afternoon on 62 minutes, directing a ball wide from just five yards.
Moments later Brad McKay missed a free header from a corner up the other end.
However the late opportunities all fell for Montrose.
Coll Donaldson made a brilliant block in the box to stop a certain goal with Morrison beaten.
Then in the final seconds, Craig Brown somehow failed to take hold of the ball in the box and let Falkirk off the hook.
Falkirk: PJ Morrison, Ryan Williamson, Coll Donaldson, Brad McKay, Sean Mackie, Finn Yeats, Stephen McGinn, Steven Hetherington, Aidan Nesbitt, Callumn Morrison, Gary Oliver.
Subs: Paddy Martin, Juan Alegria, Craig McGuffie, Leon McCann, Seb Ross, Jaime Wilson, Blair Sneddon, Kyle Connolly, Pearse Carroll.
Montrose: Ross Sinclair, Graham Webster, Kerr Waddell, Sean Dillon, Andrew Steeves, Terry Masson, Liam Callaghan, Lewis Milne, Craig Johnston, Rory McAllister, Blair Lyons.
Subs: Aaron Lennox, Paul Watson, Aidan Quinn, Mark Whatley, Adam MacKinnon, Craig Brown, Michael Gardyne, Martin Rennie, Matthew Wright.
Referee: Gavin Duncan.