A goal-less first half reflected a poor performance from both sides, although there were chances to break the deadlock.
Montrose's Steven Kerrigan had a couple of efforts on target, but they were weak shots which failedl to trouble keeper Derek Jackson.
Iain Diack could have put the home side in front after Ally Graham had headed the ball down to him in the six-yard area. However, with the goal at his mercy, the league's leading scorer pulled his shot well off target.
Montrose were the better side after the break and created several chances, although they were given a dubious penalty award when Andy Cargill went down after successfully passing to a team-mate.
Willy Martin's initial kick was well saved by Jackson, who became a home hero when he also turned Martyn Fotheringham's follow-up over the bar.
The woodwork also kept Shire in the match with Kerrigan the unlucky player, and Greig Henslee missed a sitter when he somehow turned a low cross over the bar from two yards. However, he redeemed himself in the 82nd minute when he converted a cut-back from Kerr Dodds from the same range.
Ally Graham missed a glorious chance to score for Shire when he put a shot over the bar from the edge of the area, but Shire eventually secured the point through substitute Steven Dymock.
The Montrose defence were all over the place inside the last minute, and when the ball finally dropped to Dymock he sent an angular shot whistling past the goalkeeper from the right-hand side of the box.