Ally McCoist's side thought they may have to wait at least one more week to celebrate after their lunch-time fixture was drawn but, three hours later, they were confirmed as champions when Queen's Park lost 1-0 at home to Elgin.
And Rangers were quite lucky to escape with a point from Montrose, the hosts having had a second-half goal controversially disallowed.
The Glasgow side bossed the opening stages of the game, with David Templeton looking lively on his return from injury.
Templeton drew a good save from home goalkeeper John Gibson with an audacious long-range half-volley just after the 10-minute mark and then had a goal-bound effort blocked by Stephen McNally after cutting inside from the left.
Gibson then produced another really good stop, turning a Lee Wallace shot over the box after the Rangers man had stormed into the box.
Lee McCulloch went on to drill a free-kick just wide but Montrose really began to find their feet after that and a deflected Jamie Winter shot almost bobbled past Neil Alexander in the Rangers net.
Suitably encouraged, the hosts pressed forward and Alan Campbell headed just wide from a Paul Watson free-kick.
McNalley then sent over a fantastic cross from the right wing and Martin Boyle should possibly have done better than head over the crossbar.
David Gray fired over from distance just after the break as Montrose continued to thrive, but Rangers then had their best chance for a while, Kane Hemmings latching onto a Wallace cross before turning and shooting, only for Gibson to pull out another good stop.
The match became an entertaining end-to-end affair and Montrose had the ball in the net with 25 minutes to play.
Rangers goalkeeper Alexander saved a Terry Masson volley and the loose ball was eventually hooked into the net by Boyle but the referee contentiously decided that Alexander's attempts to gather the ball had been illegally hindered by Wood.
Undeterred, Montrose continued to press for a winner and Winter's powerful low free-kick drew a decent save from Alexander.
And the hosts were awarded another free-kick on the edge of the box in stoppage-time but Alexander plunged to his left to keep out Watson's crafty effort and ensured that Rangers earned what turned out to be a title-clinching point.