Stewart Drummond gave Morecambe an early lead and the visitors were the better side in the first half.
Two goals in four minutes from Dean Moxey and Ryan Harley put the Grecians in the driving seat, but with 10 minutes left Drummond struck again to earn his side a point.
The visitors took the lead in the ninth minute when Michael Twiss whipped in a free-kick and Drummond headed home powerfully past Paul Jones.
Exeter attempted to rally and Liam Sercombe shot narrowly wide after a fine run.
The visitors were the better side in the first half and could have been further ahead at the break.
Twiss scuffed a shot inside the box and Drummond thumped the ball over the bar from close range when it looked easier to score.
Harley curled a shot just wide as Exeter chased the game. But Mark Duffy almost ruined Exeter's day at the other end when he struck a shot into the arms of the goalkeeper.
Exeter turned the game around with two goals in the first eight minutes after the break.
Moxey pulled his side level when he ran on to a through ball and took the ball around goalkeeper before slotting into an empty net.
Harley then put the Grecians ahead when he was found by Richard Logan and struck the ball superbly into the bottom corner when everyone in the ground expected a cross.
Exeter looked like they were coasting towards a crucial victory but Morecambe pulled level with 10 minutes left when Twiss found Drummond and the striker tapped home from close range.