The Grecians now have maximum points from their opening four games as they look to regain their Football League status.
And their victory extended the club's record winning run to seven matches.
But it's all gone wrong for the Lancastrians after winning their first two matches against Canvey Island and Altrincham.
However, they could easily have taken at least a point from this tough fixture.
Paul Mullin should have given Stanley a first-half advantage but his penalty, 10 minutes from half-time, was saved by Paul Jones.
Even then Andrew Mangan might have netted the rebound but conspired to shoot over the bar.
John Coleman's team did go in front with Mullin atoning for his miss.
The 31-year-old shot home left-footed to threaten the Devonians' unbeaten start. It was the first goal conceded by Exeter this season and the first since Dagenham & Redbridge found the net on April 12 last season.
It took Exeter ten minutes to restore parity as Craig Watkins beat on-loan keeper Darren Randolph for his first ever City goal.
Billy Jones then presented Chris Todd with an opportunity to head the winner 19 minutes from the end, much to the dismay of Randolph, signed from Charlton 24 hours before the game.
Accrington did enough to get a point but already Exeter look a good bet for promotion as they gained the win without being at their best.