Hiram Boateng scored his first Exeter goal to end Accrington's seven-game unbeaten run.
The former Crystal Palace midfielder lashed home on the stroke of half-time to get the Grecians back on track following back-to-back away defeats.
Pierce Sweeney converted an 86th-minute penalty to seal the 2-0 win.
Exeter's seventh home win of the season took them back to within a point of the automatic promotion places.
The hosts were quick out of the traps and created a host of chances in the opening 20 minutes.
Jake Taylor fired over the crossbar before Liam McAlinden dragged an effort past the far post.
Boateng jinked his way into the Stanley penalty area only to guide a shot inches wide of a post.
But Exeter's pressure paid dividends in first-half stoppage time after Stockley pulled the ball back for Boateng to rifle home.
McAlinden should have doubled Exeter's lead in the 49th minute after racing clear only to shoot straight at Aaron Chapman.
The striker was denied by Chapman on 80 minutes before Dean Moxey's follow-up attempt was scrambled off the line by Mark Hughes.
Sweeney made sure of the win by burying a spot-kick into the bottom corner after Hughes pulled back Stockley.