John Grant grabbed a second-half winner to ensure that Exeter failed to bounce back from last weekend's FA Cup misery.
Grant should have made it two with a penalty after a foul on Scott Davies but his effort was well saved by Grecians keeper Paul Jones.
Exeter had started brightly and went close with Daniel Seabourne heading wide after five minutes.
Aldershot finished the match with 10 men after Danny Hylton saw red for a foul on Steve Tully.
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Subs Not Used: Chalmers, Elvins, Donnelly, Newman.
Sent Off: Hylton (88).
Booked: Hudson, Davies, Morgan.
Goals: Grant 53.
Exeter: Jones, Tully, Seaborne, Taylor, Harley, Moxey, Cozic (Panther 55), Edwards (Watson 68), Basham (Obersteller 55), Stansfield, Stewart.
Subs Not Used: Marriott, Sercombe.
Booked: Taylor, Moxey.
Att: 3,784
Ref: Pat Miller (Bedfordshire).
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