Ellison provided two clinical finishes in the second half to give Jim Bentley's side a timely boost ahead of the Capital One Cup clash with Newcastle in midweek.
Ellison gave Morecambe the lead in the 46th minute when Jack Sampson swung in a delightful cross from the right wing and the unmarked Shrimps' veteran made no mistake with a header from six yards out.
The same two players combined eight minutes from time to give Morecambe a second. Sampson provided a superb pass into the area which Ellison took on his chest before he lobbed the onrushing Artur Krysiak superbly from 12 yards out.
Exeter did have chances of their own with Aaron Davies forcing Barry Roche into a scrambling save low to his left-hand side after cutting in from the left.
Roche was called upon again in the final moments of the game when he produced another fine block from the excellent John O'Flynn.
Morecambe thought they had taken the lead in the 18th minute when Sampson headed a Ryan Williams corner goalwards only for Aaron Dawson to clear off the line.