The visitors almost took the lead inside the opening 60 seconds when Matt Slater flicked the ball goalwards but he was denied by Queens Park defender Alan Trouten who cleared the ball of the line.
Montrose saw another effort cleared of the line 12 minutes later. A quick free-kick saw Euen Hall presented with an excellent chance to open the scoring but his effort was blocked on the line by Shaun Molloy.
Before the break, Queens Park skipper Daniel Ferry went close but saw his effort parried behind for a corner kick.
A fine block from Craig Smart denied Carroll in the opening minutes of the second half.
The Montrose defence struggled to clear a corner kick and the ball dropped to Carroll who looked certain to score but somehow Smart got back with a last-gasp block to defect the ball away for the corner kick.
Queens Park eventually netted the only goal of the game after 72 minutes when Carroll bundled the ball the home from close range.
Montrose keeper James Butter failed to gather a Ross Clark cross and Carroll was on hand to net from close range.