Montrose settled the better and went close on 10 minutes when a James Russell free-kick found Greig Henslee and his header was saved at full stretch by Derek Jackson.
Montrose took the lead on 14 minutes when Henslee played the ball in from the left and Jackson allowed it to slip past him and into the net at the post.
Montrose stretched their lead in the 19th minute when Henslee crossed for Gary Middleton to score with a header on the back post.
East Stirling tried to rally and on 28 minutes Carl Thywissen had a header saved by Sandy Wood.
On 30 minutes a Russell free-kick forced a good save from keeper Jackson.
Montrose were out of luck on 38 minutes when Henslee set up Kris Brash and his shot smacked against the post.
Montrose went close again on 42 minutes when Barry Donnachie put Middleton through and he shot wide from a good position.
On 62 minutes Stephen Fraser set up Calum Watson and he shot wide on the run.
Montrose went close again on 67 minutes when Jackson saved well at the feet of Watson and a follow-up from Middleton was deflected for a corner.
East Stirling were out of luck on 74 minutes when Thywisson pulled the ball back for Mark McKenzie to shoot against the post from close range.
Montrose finished on top and on 80 minutes an effort from Ian McLeod was fumbled by Jackson, but the keeper recovered to gather before Phil Reid could connect.