Pierce Sweeney's header was enough for Exeter to see off Reggie Lambe and his Carlisle United teammates and move back to the top of the Sky Bet League Two table.
A header just after half-time by defender Sweeney added to Carlisle's miserable home form.
Carlisle skipper Danny Grainger was inches away from finding the target with an early effort, but it was Exeter who carried the main threat with Jayden Stockley's overhead flick hitting a post and Reuben Reid forcing a fingertip save from Jack Bonham with a rasping drive from the edge of the area.
Carlisle's first-half build-up play was neat enough without directly troubling Christy Pym in the Grecians' goal, although Hallam Hope was a fraction away from making contact with a driven Shaun Miller cross inside the six-yard box.
Exeter went in front in the 49th minute when Sweeney forced a corner on the right and was on hand to nod home from a couple of yards when the resulting kick came to him after Troy Brown's flick had left Bonham flat-footed.
The goal sparked a response from the home side and after Pym had clawed away a Luke Joyce shot at the near post, Dean Moxey came to the Grecians' rescue with a goal-line clearance from a Miller header.
Pym saved at point-blank range from Clint Hill, and although Nicky Adams fired in a barrage of crosses from the left, City's defence held firm.