They threatened after two minutes when a looping shot from Greg Miller was well saved by Jim Butter. Montrose hit back, and two minutes later James Russell had a shot kept out by Mark Peat.
In the tenth minute a 30-yard drive from Alan Brazil was well saved by Butter.
After 16 minutes a curling effort from Jay Stein went just wide, then in the 33rd minute an overhead kick from Matthew King landed on the roof of the Montrose net.
The game boiled over after 44 minutes when Brazil was sent off for an alleged elbow on Jamie McKenzie.
When the second half began, Butter twice denied King, the first occasion coming out of his box.
Arbroath appealed for a penalty five minutes later when a shot from Stephen Cook seemed to strike a hand.
The visitors took the lead in the 63rd minute when Jay Stein beat Butter with a deft lob.
Montrose missed a great chance to equalise after 68 minutes when McKenzie was pushed in the box by Miller. Martyn Fotheringham fired the penalty kick over the cross bar.
Arbroath went back on the attack and almost made it 2-0 after 80 minutes when the ball came off the head of defender Paul Doyle and looped inches wide of the post.
Montrose had one last chance to equalise in stoppage time when Elliott Smith played the ball into the box and McKenzie shot over on the turn.