Full-time: Robins 1, Exeter City 2
Cheltenham Town slipped to their first defeat in four games, leaving them in the relegation zone with eight matches remaining.Goals from Tom Nichols and Graham Cummins put Paul Tisdale's play-off chasers 2-0 up before a late own goal restored hope for the Robins.
There was a late push, with substitute Joe Hanks forcing Christy Pym into a low save, but Cheltenham ran out of time.
Cheltenham made a promising enough start, with the returning Wes Burns firing wide after Danny Haynes' pass, but they lost their way and Exeter controlled much of a largely uneventful first half.
They opened the scoring in the 26th minute when a long kick from Pym was helped on by David Wheeler and Nichols lifted the ball delicately over the head of the advancing Trevor Carson.
Carson saved well from half-time substitute Tom McCready in the 58th minute, but Cheltenham showed an improvement in the final 20 minutes, helped by the introductions of Hanks and Omari Sterling-James from the bench.
But Exeter made their task doubly difficult in the 86th minute, when Cummins capitalised on an error from Carson, who did not deal with a shot from Arron Davies after a short corner routine.
A shot from Lee Vaughan was deflected into his own net by Jordan Moore-Taylor in the 89th minute and several scrambles followed in the box, but Cheltenham could not find a leveller and they must dust themselves down ahead of next Saturday's home match against Plymouth Argyle.
Cheltenham Town (4-5-1): Carson; Berry (Vaughan 79), Taylor, Packwood, Braham-Barrett; Burns, Mills, Sparrow (Hanks 72), M Richards, Haynes (Sterling-James 72); Harrad. Subs not used: Gould, Kotwica, Wynter, Deaman.
 Exeter City (4-3-3): Pym; Davies, Ribeiro, Moore-Taylor, McAllister; Oakley, Sercombe (McCready 46), Harley; Wheeler (Holmes 68), Cummins (Morrison 86), Nichols. Subs not used: Hamon, Bennett, Keohane, Reid.
Referee: Darren Drysdale
Attendance: 2,880 (584 away).