The Grecians stand alone at the top of the Conference for the first time after making the perfect start to the new season.
Two first-half goals from Lee Phillips and Chris Todd were enough to secure another maximum for the Grecians.
Exeter looked bright in the opening stages. Phillips headed a Billy Jones corner over the bar before the latter curled a free-kick from the edge of the box over the bar in the opening minutes.
Morecambe's best early chance came when Paul Jones failed to clear a Wayne Curtis corner and James Bentley struck the ball against the post.
Midway through the half Jon Challinor's cross was half-cleared and Phillips scrambled the ball home from close range.
Morecambe almost pulled level instantly. Paul Jones made up for his earlier mistake when he pulled off a fine save to keep out Darren Kempson's point-blank header from Curtis' corner.
But it was the Grecians who increased their lead just after the half-hour mark.
Challinor's long throw was headed out by Bentley but his clearance fell to Todd who struck a fine right-foot volley from 20 yards into the bottom corner.
After the break Phillips almost made it three for Exeter when he headed just wide from Paul Jones' cross. It was an open game with lots of chances. Kempson headed inches wide for the Shrimps who created a host of chances.
Phillips again went close for Exeter with a shot into the side-netting but the hosts held on to secure another maximum.