David McMillan and Declan McManus struck either side of half-time to give the Bairns the advantage but they were brought level by Terry Masson and Graham Webster's penalty before a late, late winner from Aidan Connolly.
It could prove a vital strike from the little winger as elsewhere along the east coast table-ropping Raith Rovers were losing to Dumbarton while Clyde clipped the wings of Airdrie.
That leaves Falkirk a point off the summit, yet in FOURTH position with 31 points and all above on 32.
But they had to bring the momentum of the Mo, the division's form team, to a halt and they took their time to get into stride.
MATCHDAY BLOG: How it happened - Montrose v FalkirkThe home side were dangerous on the break with trickery on show from Graham Webster and Martin Rennie, but in truth Falkirk played like the home side, constantly on the attack, dictating the play with Stewart Petrie's side picking and choosing their times to defend or break.
They did have the best chance of the opening exchanges when Webster sold Paul Dixon on the wing and curled a great effort that was tucking inside the post until Robbie Mutch's outstretched arm beat it away to safety.
Falkirk captain Gregor Buchanan hooked an effort over from a Michael Tidser corner and Martin Rennie was denied on the breakaway by Gary Miller after a lovely turn to deceive Tidser in midfield.
The Bairns' build-up and work-rate was impressive but on a slippery surface the final ball was not quite falling, especially for David McMillan. But the Irishman finally made his hard work count with a backpost header to convert a Louis Longridge cross six minutes before the break.
It was deserved on the balance of play and Falkirk looked out of sight after bursting into life for the second half, with McManus desparate to get on the scoresheet.
The loanee burst down the right and fired a shot from a tight angle off the outside of the post but he got on the scoresheet seconds later when he rolled his marker and tucked the ball inside the post from the edge of the box.
The Bairns looked out of sight by then, and McManus could have had another with a lovely little clipped finish over Aaron lennox that skidded just wide but the Mo's momentum picked up shortly after the houtr mark and they made it count.
Terry Masson forced over the line from a goalmouth scramble despite a despairing lunge from Lewis Toshney on the line to boot the ball away. Gavin Duncan adjudged it had crossed and the home side took the initiative.
Only a brave low block at his post by Mutch denied substitute Ross Campbell and kept the Bairns ahead and the Falkirk managerial duo made a formation change from the 3-5-2 to a 4-3-3 and then a 4-4-2.
But it wasn't enough to deny the home side an equaliser when Graham Webster fired the leveller with eight minutes to go from the penalty spot after a soft call from ref Gavin Duncan penalised a barge from Michael Doyle.
With the clock running down it looked ominous until Aaron Lennox spilled a corner at his near post and the ball was lashed in by substitute Aidan Connolly, sparking enthustastic celebrations from the away terracing as the winger ran to the corner cupping his ears.