The Grecians failed to sparkle in front of a large crowd during the first half and went behind to Neil Redfearn's superb free-kick.
But teenager Dean Moxey pulled the Grecians level when he nodded home Alex Jeannin's corner six minutes after the break and they dominated the game from that moment.
Steve Flack gave Exeter the lead with a fine strike just after the hour mark before Sean Devine made sure from the penalty spot in the dying minutes.
Rookie goalkeeper Paul Jones made a string of fine saves to keep lively Scarborough at bay and the three points were well deserved.
Exeter started brightly and could have gone ahead in the third minute.
Gareth Sheldon's corner was only half-cleared and Jeannin's goalbound shot was cleared off the line by Redfearn.
Scarborough went ahead with their first shot on target midway through the first half when Redfearn's sweetly struck free-kick found the net.
On the stroke of half-time Flack headed narrowly wide from Jeannin's cross.
Shortly after the break Keith Gilroy forced Jones to make a fine save with a strike from 35 yards.
In the 51st minute Exeter were level. Jeannin drilled in another fine corner and teenager Moxey glanced a delicate header past the goalkeeper.
Exeter were now well on top. Sheldon went close with a powerful strike from inside the box before the Grecians took the lead just after the hour mark.
Devine picked out Flack with a fine throughball and the giant striker struck a fine low shot past the goalkeeper from 12 yards.
Chris Senior shot wide from close range for Scarborough before Exeter finally made sure with two minutes left on the clock.
Devine's cross was nodded down by Flack and Redfearn was harshly adjudged to have handled inside the box. Devine stepped up and made no mistake from the spot.