Montrose dominated the early stages and the Shire defence was given a severe examination during the opening 15 minutes.
The visitors created and missed several opportunities with Craig Smart and Martin Wood missing glorious chances to break the deadlock.
Shire keeper Derek Jackson kept his side in contention with important saves from a Kevin Webster free-kick which he caught under the bar and two blocks with his legs to deny Wood a possible double.
Shire's lone strike during a goalless first half came from Derek Ure whose shot hit keeper Michael Hankinson in the legs and bounced clear.
Shire's first-half defensive success came to nothing three minutes after the restart when Smart put Montrose in front from the penalty spot after Jamie Mackay had upended Graeme Sharp.
Shire equalised within 10 minutes with a stunning volley from Ure after Joe Robertson had picked him out with an accurate flag-kick.
Shire looked the likelier side for about 15 minutes when Montrose manager Henry Hall pulled off what became a winning substitution.
Watson's contribution to the game was a mere 10 minutes of play but he gave his side all three points with a well-taken goal in the final minute.
Once again to their cost Shire had conceded a late goal to miss out on a share of the points.