Matt Gill put the Grecians ahead from the penalty spot after Neil Austin was adjudged to have handled inside the box. Substitute Craig McAllister then made sure with a powerful header in the closing stages.
Steve Basham came close to giving the Grecians an early lead when he met Dean Moxey's deep cross but dragged his shot narrowly wide at the far post.
Darlington, who went into administration and were docked ten points this week, had a couple of early chances and Paul Jones spread himself well to deny Pawel Abbott.
Franz Burgmeier tried his luck from the edge of the box for Darlington but it was another comfortable save for Jones.
After the break Carl Tremarco thumped a free-kick over the bar from 25 yards for the visitors as both sides chased a winner.
Substitute Richard Logan almost made an instant impression when he had a header saved on the line by Darlington goalkeeper Andy Oakes.
Exeter finally broke the deadlock in the 72nd minute. Austin was harshly adjudged to have handled as he blocked Matt Taylor's close-range shot. Gill stepped up to take the penalty and slotted the ball past Oakes.
McAllister should have made it two shortly afterwards but failed to steer the ball past Oakes from close range. Basham then headed a cross from Neil Saunders past the post with only the goalkeeper to beat.
In the closing stages Logan met Moxey's cross and his bullet header was superbly saved by Oakes.
Moxey then picked out McAllister and the striker's header flew past Oakes for a well-deserved second.
White was sent off in the closing minutes after picking up a second yellow card to cap a miserable week for Darlington.