Montrose opened the scoring on five minutes when Andy Rodgers broke on the left and fired a shot against the cross bar and team captain Steven Kerrigan drove home the rebound.
Montrose should have stretched their lead on sixteen minutes when a long ball from Chris Tawse released Rogers and he shot wide with just the goalkeeper to beat.
The home pressure continued and when Scott Michie crossed from the byline Stewart Cumming shot just wide. Then a minute later Cumming crossed for Michie to have a first time effort saved.
Elgin threatend on thirty four minutes when a drive by David Hind flew just wide of the post.
Montrose made it 2-0 on thirty seven minutes when Rodgers released Michie and he shot past the unprotected Keiron Renton.
Elgin attacked at the start of the second half and John Farquhar turned a Chris Gardiner drive round the post.
On fifty six minutes Farquhar was in action again saving well at the feet of Paul Kaczan.
Montrose went back on the attack and on 69 minutes Chris McLeod headed over from a Paul Napier corner.
On seventy nine minutes Rodgers ran clear and his shot was saved by the feet of Renton.
A minute from time Rodgers ran clear again and this time his shot went inches wide of the post.
Three minutes into stoppage time Kerrigan headed against the post for Montrose and a follow up effort from John Adam was cleared off the line.