Adam Stansfield put the Grecians ahead midway through the first half before Matt Taylor made sure with a late header.
It could have been more comfortable but Richard Logan failed to convert from the penalty shot midway through the second half.
Chester started brightly and Ryan Lowe shot narrowly wide after a neat move in the opening minutes. Kevin Ellison then forced Paul Jones to save well with a low strike from 25 yards.
Stansfield had Exeter's best early chance when his deflected shot from a tight angle was saved by John Danby.
Exeter took the lead midway through the half. Dean Moxey picked out Marcus Stewart inside the box and, when the ball was struck across the face of goal, Stansfield tapped the ball home from close range.
Exeter grew in confidence after the goal and began to dominate, and the impressive Moxey had a powerful shot well saved by Danby.
Chester came close to an equaliser when Ellison curled in a free-kick from the edge of the box but the shot was tipped over the bar by Jones.
After the break Ellison volleyed over the bar for Chester as the visitors threw men forward. At the other end Bertrand Cozic swapped passes with Stansfield and struck the ball past the post from close range.
Logan's penalty was saved by Danby after Kevin Roberts had been harshly adjudged to have handled Stansfield's close-range shot.
Exeter continued to push forward and Stewart struck a long-range shot narrowly wide after a fine run.
Rob Edwards attempted to lob Danby with a 40-yard free-kick but the goalkeeper held on to the ball. With three minutes left Taylor rose well to meet Edwards' cross and he headed home from close range.