Johnstone opened the scoring with a close-range tap-in on eight minutes.
The 21-year-old slotted Bobby Barr's cross into the bottom corner for his 14th goal of the season to make it 2-0, before Paul McMullan added a third.
Dale Hilson and Gary Oliver hit back for the visitors but Morton held on for the win.
Denny Johnstone netted a first-half brace as Morton returned to winning ways with victory over Queen of the South.