A goal in each half meant honours were even in an entertaining first game of the season.
Exeter took an early lead through Sean Devine but they sat back and it came as little surprise when Morecambe pulled level through Michael Stringfellow in the closing stages.
City were ahead within five minutes. Michael Howard made a hash of his clearance inside the box and when the ball fell to Devine he made no mistake with a fine low strike under the goalkeeper from 12 yards.
Les Afful and Gareth Sheldon provided a constant threat for the Grecians. Sheldon went close with a long-range shot past the post and Devine was denied when Keiron Walmsley scrambled his shot off the line.
Sean O'Connor thought he had pulled the Shrimps level midway through the half but his deflected shot past Martin Rice was ruled out for offside.
Afful went close for Exeter before Terry McFlynn headed just wide for the Shrimps on the stroke of half time.
After the break Jake Edwards thumped a volley over the bar for the Grecians after he was found by Alex Jeannin.
Jim Bentley almost pulled Morecambe level when he met Michael Twiss' centre but headed the ball against the crossbar.
At the other end Sheldon rose well to meet Scott Hiley's cross, but his header was well saved by Adam Sollitt.
Morecambe pulled level with just eight minutes left on the clock. Garry Hunter drifted in a free-kick from the right and substitute Stringfellow rose highest to nod the ball home.
The goal was no more than they deserved for a spirited second half performance.