East Fife were the better side in the first half and went close on nine minutes when Jim Butter dropped a Gavin Beith cross but gathered the ball at the second attempt before Craig Lumsden could connect.
East Fife were out of luck on 14 minutes when Fraser Duncan headed against the cross bar from a Beith corner.
Montrose tried to rally and on 25 minutes when Kevin Webster went on a run and fired a shot just wide.
On 33 minutes it was the turn of Graeme Sharp to run at the East Fife defence but his effort was blocked.
On 36 minutes a lob from Steven Nicholas was net-bound until Sharp got back to head off the line. East Fife were out of luck again on 41 minutes when Jonathan Mitchell robbed Neil Stephen on the by-line and hit the post from a tight angle.
A minute from the break a 35-yard free-kick from Martin Wood was saved by John Dodds.
Montrose pressed in the start of the second half and Calum Watson had a shot deflected wide of the post. Then two minutes later Watson was in again but shot against Dodds when a pass to Sharp looked the better option.
East Fife took the lead on 54 minutes when a simple through ball opened the home defence and Mitchell pounced to score.
It was 2-0 on 59 minutes when Leslie Byle volleyed home a cross from Sean Paliczka.
Montrose began a fight back six minutes from time when Sharp cut in from the right and scored with a low drive.
Montrose pressed for an equaliser and Ross Graham missed his kick from a Sharp cross, then with the 90 minutes up Sharp was denied by goalkeeper Dodds.
Three minutes into stoppage time Stephen headed the ball forward and Sharp scored with a hook shot for a dramatic equaliser.