Crawley Town conceded two second half goals which brought their third home defeat in a row.
The visitors took the lead five minutes into the second half when Ollie Watkins struck a shot from the area which was deflected into the net.
Exeter added a second goal with 23 minutes to go through Jordan Moore-Taylor.
Mark Connnolly pulled a goal back at the end eith a headed goal to created an exciting finish as Crawley fought to rescue a point.
Reds made just one change with Lewis Young starting at right wing-back in palce of Josh Lelan, who went off injured against Wycombe.
Exeter made three changes from the side which drew 2-2 at home to Blackpool with goalkeeper Bobby Olejnik, Ollie Watkins and Reubin Reid all included.
The Grecians made a bright start with Ollie Watkins finding Lloyd James in the area from a free-kick, but he put his shot just wide.
Watkins then had another go from a run along the edge of the area which he skied well over the bar.
Connolly made intervened well to clear a cross into the area by Dave Wheeler.
Reds got into the game more as the half progressed and had a series of useful attracks and chances to score as Dean Cox twice came close to finding James Collins with dangerous crosses and Henderson played in Andre Blackman, only for the visiting defence to clear.
Just before half-time came a really good chance as Enzio Boldwewijn played a one-two with Smith, only for the keeper to claim the attempted chip.
Exeter took a 50th minute lead through a deflected shot by Watkins.
Dermot Drummy made an immediate change byt bringing on striker Rhys Murphy in place of Djalo and playing him alongside Collins up front.
Watkins went close again before Exeter's Jordan Taylor-Moore made made it 2-0 with in the 67th minute.
Taylor took advantage of a mistake from the the defence and crossed to Moore-Taylor to put away.
Reds looked like they had done enough to score as late consolation when Boldewijn's header was parried by the keeper.
Then monents later in the 90th minute Connolly put the ball in the net with a firm header from a corner to make it 1-2.
REDS: Morris, Young, Connolly, Boldewijn, Smith (capt) (Payne 76), Blackman, Collins, McNerney, Djalo (Murphy 52), Cox (Clifford 73), Henderson
Unused subs: Mersin, Yorwerth, Garnett, Bawling
EXETER CITY: Olejnik, Woodman, James, Harley, Wheeler (Oakley 84), Watkins, Moore-Taylor, Taylor, Stacey, Reid (McAlinden 68), Brown
Unused subs: Tillson, Grant, Hamon, Croll, Sweeney
REFEREE: Dean Whitestone
ATTENDANCE: 1,826 (362 away)
CRAWLEY OBSERVER MAN OF THE MATCH: Joe McNerney