Accrington though managed to score with pretty much their only two real attempts on goal.
City had a string of opportunities but were denied by a combination of goalkeeper Paul Crichton's acrobatics and some poor finishing.
The defeat was a setback to Exeter's hopes of reaching the play-offs in a bitterly frustrating afternoon at St James's Park in front of more than 4,000 fans.
The visitors took the lead with their first attack of the game after only eight minutes.
Danger man Lee McEvilly was picked out by strike partner Paul Mullin and he scampered forward before drilling a low strike past Paul Jones from ten yards for his 15th goal of the season.
Exeter looked nervous at the back in the early stages as they struggled to contain the visitors in the blustery conditions.
The game entered a scrappy period before Exeter eventually pulled level midway through the half.
Sean Devine's cross fell to Dean Moxey and when the youngster's shot flew back off the crossbar Jake Edwards tapped the ball home from close range.
Devine then struck a fierce free-kick over the bar from 20 yards and had two long-range efforts saved by Crichton.
After the break Les Afful was twice denied by Crichton and also blasted the ball over the bar from only six yards.
Alex Jeannin then had a header saved by the goalkeeper but Accrington took the lead completely against the run of play just before the hour mark.
Crichton's long kick carried in the wind and when Santos Gaia misjudged his header McEvilly coolly slotted the ball past Jones from close range for his second of the game.
Edwards summed up Exeter's afternoon when he thumped the ball over the bar from six yards with only the goalkeeper to beat - and there was no way back for City.