Paul Tosh had the ball in the net on two occasions only to be denied by offside flags and this proved crucial as defensive slackness gifted the visitors two second half goals.
Montrose made two changes to the 11 which started against Hibs in the
cup. John Maitland and Hugh Davidson dropped out and in came Aaron Sinclair and Tosh. Sean Fleming was fit enough to start at left-back with Stephen McNally at right-back.
Montrose lined up with an attacking 4-3-3 formation. Milligan, Hegarty and Sinclair were in midfield, with Nicholas just behind a front pair of Gemmell and Tosh.
Gaffer Steven Tweed was fit enough for a place on the bench, alongside Nicol, Tomana, Leyden and Coutts.
Montrose made a bright start and in the opening minute, Crighton met a Sinclair corner. His first effort was blocked and his second went wide.
In four minutes, Gemmell drove wide from a free-kick.
The home side continued to make the running and Fleming cut the ball back to Hegarty and he drove wide.
Queen's threatened for the first time when they were wrongly awarded a corner. Douglas sent in the corner and McNeil just kept the ball out on the near post.
Montrose raced to the other end and Sinclair crashed a first-time volley wide of the target, then Gemmell headed wide from a Tosh cross.
Montrose took a deserved lead in 36 minutes. A Gemmell shot was parried by McGeown and Paul Tosh followed up to score.
Three minutes later, Montrose almost scored a second goal when they were awarded a free-kick 40 yards out. McNally surprised everyone by trying a shot and McGeown was fortunate to scramble the ball round the post.
Sean Fleming had taken a knock at he was replaced at half-time by Nicol. Sinclair dropped to left-back with Nicol in midfield.
Two minutes into the second half, Daly headed wide from a Douglas corner, then in 51 minutes, Walker was booked for a foul on Sinclair.
Queen's Park equalised in 52 minutes with a goal the home defence will want to forget. They failed to deal with a long ball through the middle and Murray nipped in to chip over McNeil.
Five minutes later, Murray almost scored a second, but his header was headed off the line by Nicol.
Montrose thought they were back in front in 59 minutes when Tosh shot home, but the linesman's flag was raised. It was a poor decision as Gemmell was in an offside position but Tosh was not. Tosh raced to vent his anger at the linesman and was booked.
In 64 minutes, a fierce shot from Tosh was saved at his post by McGeown.
In 69 minutes, Gemmell was booked as Montrose prepared to defend a corner. When the corner came in, Montrose couldn't get the ball clear and Quinn shot home from the edge of the box.
Montrose were shocked but they buckled down and in 74 minutes, Tosh drilled the ball into the net from a Sinclair pass, but was again offside. The linesman's decision was once again debatable as Tosh again seemed to come from a deep position.
The home side never looked like scoring and in 85 minutes, McNeil saved at the feet of Daly.
Tomana went on for Milligan and Montrose had one last chance in the 89th minute when Tosh shot over on the turn.
Montrose: McNeil 7, McNally 7, Sinclair 7, Hegarty 6, Campbell 6, Crighton 6, Milligan 7 (Tomana), Nicholas 6, Tosh 7, Gemmell 7, Fleming 6 (Nicol). Subs: Tweed, Leyden, Coutts.