In a game of few chances, Yeovil were denied what would have been the winning goal in the second half when Tom Eaves' header hit the crossbar.
Exeter went close in the first half when Reuben Reid was put through on goal, with Artur Krysiak forced to rush out and clear the danger.
Ollie Watkins also threatened for the visitors when his fierce drive from 25 yards only just passed the crossbar.
There were bizarre scenes at the end of the opening period as a whistle from the crowd was mistaken by everyone for the half-time signal. It resulted in mass confusion around Huish Park as referee Tim Robinson was forced to bring the players back onto the pitch before playing the remaining few seconds of the half.
Yeovil had a penalty claim turned down early in the second after the ball appeared to strike the arm of Exeter's Jordan Moore-Taylor in the box.
There then followed a golden chance for Yeovil when Ryan Dickson found Eaves with a peach of a cross, but the header looped past the helpless Christy Pym and cannoned off the bar.
Substitute Liam McAlinden went close for the visitors in the closing stages but Krysiak was equal to his shot.
Report supplied by the Press Association
Match ends, Yeovil Town 0, Exeter City 0.
Second Half ends, Yeovil Town 0, Exeter City 0.
Foul by Otis Khan (Yeovil Town).
Joel Grant (Exeter City) wins a free kick in the attacking half.
Tom Eaves (Yeovil Town) is shown the yellow card.
Foul by Otis Khan (Yeovil Town).
Jake Taylor (Exeter City) wins a free kick in the attacking half.
Tom Eaves (Yeovil Town) wins a free kick in the defensive half.
Foul by Ryan Harley (Exeter City).
Corner,  Exeter City. Conceded by Ryan Dickson.
Liam Shephard (Yeovil Town) wins a free kick in the defensive half.
Foul by Joel Grant (Exeter City).
Nathan Smith (Yeovil Town) is shown the yellow card for a bad foul.
Foul by Nathan Smith (Yeovil Town).
Jake Taylor (Exeter City) wins a free kick on the right wing.
Corner,  Yeovil Town. Conceded by Jack Stacey.
Substitution, Exeter City. Joel Grant replaces Lee Holmes.
Substitution, Yeovil Town. Francois Zoko replaces Ben Whitfield.
Matt Butcher (Yeovil Town) is shown the yellow card for a bad foul.
Foul by Matt Butcher (Yeovil Town).
Ryan Harley (Exeter City) wins a free kick in the defensive half.
Attempt missed. Tom Eaves (Yeovil Town) left footed shot from the right side of the box is close, but misses to the right.
Attempt saved. Liam McAlinden (Exeter City) right footed shot from the left side of the box is saved in the bottom left corner.
Alex Lawless (Yeovil Town) wins a free kick in the attacking half.
Foul by Ollie Watkins (Exeter City).
Foul by Ryan Dickson (Yeovil Town).
Lloyd James (Exeter City) wins a free kick in the defensive half.
Liam McAlinden (Exeter City) is shown the yellow card for a bad foul.
Alex Lacey (Yeovil Town) wins a free kick in the attacking half.
Foul by Liam McAlinden (Exeter City).
Foul by Nathan Smith (Yeovil Town).
Liam McAlinden (Exeter City) wins a free kick on the right wing.
Attempt missed. Lee Holmes (Exeter City) right footed shot from outside the box is close, but misses to the right.
Attempt saved. Liam McAlinden (Exeter City) left footed shot from the right side of the box is saved in the centre of the goal.
Substitution, Exeter City. Liam McAlinden replaces Reuben Reid.
Attempt missed. Otis Khan (Yeovil Town) right footed shot from outside the box is close, but misses to the right.
Tom Eaves (Yeovil Town) hits the bar with a header from the centre of the box.
Corner,  Yeovil Town. Conceded by Jack Stacey.
Corner,  Exeter City. Conceded by Liam Shephard.
Corner,  Yeovil Town. Conceded by Jake Taylor.
Yeovil and Exeter played out an uninspiring goalless draw at Huish Park.