The 37-year-old winger's neat finish capped off a lovely move from the Shrimps in the 55th minute to continue their impressive start to the season.
Jack Dunn and substitute Lee Molyneux combined well with the latter sending Ellison though on goal and he side-footed past Glovers goalkeeper Artur Krysiak.
Morecambe had their keeper Barry Roche to thank for taking maximum points.
He tipped away a first-half header from Tom Eaves and then pushed a Matty Dolan piledriver onto a post.
In stoppage-time, Roche also pushed wide powerful shots from substitute Tahvon Campbell and a Dolan free-kick from 25 yards.
Ellison nearly helped himself to a brace in the 62nd minute but Krysiak managed to tip his header wide. Molyneux was again the provider, sending a perfect cross to the back post, but the winger failed to convert.
Report supplied by Press Association.
Match ends, Yeovil Town 0, Morecambe 1.
Second Half ends, Yeovil Town 0, Morecambe 1.
Corner,  Yeovil Town. Conceded by Barry Roche.
Attempt saved. Matthew Dolan (Yeovil Town) right footed shot from outside the box is saved in the top right corner.
Tahvon Campbell (Yeovil Town) wins a free kick in the attacking half.
Foul by Andrew Fleming (Morecambe).
Bevis Mugabi (Yeovil Town) wins a free kick in the defensive half.
Foul by Rhys Turner (Morecambe).
Attempt saved. Aaron McGowan (Morecambe) left footed shot from outside the box is saved in the top left corner.
Attempt missed. Tom Eaves (Yeovil Town) right footed shot from the centre of the box is too high.
Attempt saved. Tahvon Campbell (Yeovil Town) right footed shot from outside the box is saved in the top right corner.
Foul by Tahvon Campbell (Yeovil Town).
Alex Whitmore (Morecambe) wins a free kick in the attacking half.
Foul by Nathan Smith (Yeovil Town).
Kevin Ellison (Morecambe) wins a free kick on the right wing.
Matthew Dolan (Yeovil Town) wins a free kick on the left wing.
Foul by Andrew Fleming (Morecambe).
Matt Butcher (Yeovil Town) wins a free kick in the attacking half.
Foul by Andrew Fleming (Morecambe).
Substitution, Yeovil Town. Omar Sowunmi replaces Ryan Dickson.
Corner,  Yeovil Town. Conceded by Alex Whitmore.
Tahvon Campbell (Yeovil Town) wins a free kick in the attacking half.
Foul by Alex Kenyon (Morecambe).
Substitution, Morecambe. Aaron McGowan replaces Cole Stockton.
Andrew Fleming (Morecambe) is shown the yellow card for a bad foul.
Ryan Dickson (Yeovil Town) wins a free kick in the attacking half.
Foul by Andrew Fleming (Morecambe).
Substitution, Morecambe. Rhys Turner replaces Jack Dunn.
Foul by Francois Zoko (Yeovil Town).
Luke Conlan (Morecambe) wins a free kick in the attacking half.
Ryan Dickson (Yeovil Town) wins a free kick on the left wing.
Foul by Jack Dunn (Morecambe).
Attempt missed. Nathan Smith (Yeovil Town) right footed shot from the centre of the box misses to the right.
Corner,  Yeovil Town. Conceded by Alex Kenyon.
Attempt missed. Nathan Smith (Yeovil Town) header from the left side of the six yard box is high and wide to the left.
Corner,  Yeovil Town. Conceded by Andrew Fleming.
Tom Eaves (Yeovil Town) wins a free kick in the defensive half.
Foul by Alex Whitmore (Morecambe).
Substitution, Yeovil Town. Tahvon Campbell replaces Ryan Hedges.
Substitution, Yeovil Town. Francois Zoko replaces Otis Khan.
Kevin Ellison's second-half strike sent Morecambe to the top of the early League Two table as they claimed victory at Yeovil Town.