Shire went into the tie as heavy favourites against a Fort William side sitting bottom of the Highland League without a point.
But Derek Ure' s side had to wait until first-half stoppage time to make the breakthrough, Jamie Hamilton slotting home in the fourth minute of added time.
However the home side doubled their advantage just seven minutes after the restart as Connor Greene's header from Hamilton's cross set up the opening for Tyler Fulton.
Any hopes of an unlikely comeback from the visitors were ended 20 minutes from time as another Greene header from a corner found Kevin Turner who third.
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The majority of the first round tie take place on Saturday with Camelon, away to Dunbar United, among the teams seeking to join Shire if the second round draw