Although the victory was by a narrow 1-0 margin, they thoroughly deserved to take all three points on the strength of their first half showing in which they dominated in every department.
They might have taken the lead as early as the second minute, but Barry Donnachie rescued his side with a goal-line clearance from Stephen Oates before Michael Hankinson kept Shire out with a flying save from Steven Dymock.
Shire's pressure had to pay off sooner or later, and the deadlock was broken in the 20th minute. Andrew Brand provided the cross into the box, Carl Thywissen's powerful header was blocked by another goal-line clearance from Donnachie, but this time Dymock latched on to the rebound to head into the net past the stranded Hankinson.
Montrose improved after the break and took control of the midfield as Shire began to tire after their efforts in the first half.
Montrose created a few opportunities, but lack of finishing power up front kept the score in Shire's favour.
Although Euan Hall might have grabbed an equaliser near the end, it would have been an injustice on the home side if they had not taken all three points.