The home side enjoyed the bulk of early possession, but it was Montrose who opened the scoring in the 16th minute with their first serious attack. The Arbroath defence failed to clear their lines and a Chris McLeod shot broke to Scott Michie, who slotted the ball home from eight yards.
Arbroath responded immediately, Roddy Black equalising with a 30-yard rocket which flew high into the top right-hand corner of the net.
Arbroath continued to dominate with Barry Sellars, Willie Martin and Jay Stein all linking up well to create the Montrose defence numerous problems.
Steven Rennie came close to putting Arbroath ahead on the stroke of half-time with an angled 20-yard shot which Reid parried. The keeper then did well to block a follow-up shot from Sellars.
Arbroath's domination finally paid off six minutes into the second half when Stein fired them into the lead.
Substitute Jon Voigt, who had only been on the field for two minutes, then put the result beyond doubt when he tapped the ball home from six yards after being set up by Alan Brazil.
Montrose struggled to make any impression, although Chris Tawse came close with a header which hit the side netting.
Arbroath's Andy Reilly directed his header wide from a few yards out, then Voigt guided the ball narrowly past the far post after leaving the Montrose defence for dead.