The visitors were rewarded after the break when David Murray lobbed Montrose keeper Andrew McNeil and then piled on the pressure in search of a winner.
Anthony Quinn lashed in from 12 yards out, firing the ball into the top of the net with 20 minutes remaining.
Montrose: McNeil, McNalley, Cambell, Crighton, Sinclair, Milligan (Tomana 84), Hegarty, Nicholas, Fleming (Nicol 46), Tosh, Gemmell. Subs Not Used: Coutts, Tweed, Leyden.
Booked: Tosh, Gemmell.
Goals: Tosh 35.
Queens Park: McGeown, Walker, Little, Brough, Douglas, Chris Hamilton (Martin 66), Stewart, Anthony Quinn, McBride, Daly, Murray (Watt 85). Subs Not Used: Gordon McPherson, Gallagher, Henry.
Booked: Walker.
Goals: Murray 51, Anthony Quinn 69.
Att: 325
Ref: J Beaton
Source: BBC Sport
Source: BBC Sport