Gavin Morrison finished from close range to put Elgin further ahead four minutes after the break.
Two late Craig Gunn goals sealed the win, the first from just inside the area and the second from closer in.
Montrose: McNeil, McNalley, Crighton, Cambell, Sinclair, Milligan (Nicol 76), Hegarty, Davidson, Nicholas (Boyle 86), Tosh, Gemmell (Tomana 71). Subs Not Used: Coutts, Tweed.
Sent Off: Hegarty (42).
Booked: Hegarty, McNalley, Nicol.
Elgin: Gibson, Niven (Edwards 71), Kaczan, Inglis, David W Craig, Gavin Morrison, Nicolson, Crooks, MacAulay (Smith 80), Sutherland, Frizzel (Gunn 68). Subs Not Used: Dunn, Cameron.
Booked: Niven, Kaczan.
Goals: Sutherland 45, Gavin Morrison 49, Gunn 90, 90.
Att: 280
Ref: B Colvine
Source: BBC Sport
Source: BBC Sport