The visitors began positively and came mighty close to a goal less than a minute in. Craig McAllister powered in a header that appeared to be blocked on the line by his fellow striker Adam Stansfield.
McAllister then hooked a shot narrowly wide from a long punt forward from keeper Paul Jones.
The Grecians deservedly went in front after six minutes. McAllister's flick fell perfectly for Stansfield and he lashed home clinically from 15 yards.
Jimmy Ryan lifted a shot over the top as Stanley finally made some inroads, then John Miles saw a half-volley flash past the far post.
The hosts had started to boss proceedings and they hit back to level after 34 minutes. Skipper Peter Cavanagh played a short corner-kick to Miles, and he side-stepped Dan Seaborne before crashing home a super angled drive from just inside the box.
Midfielder Matt Gill missed a great chance for Exeter as they almost responded within a minute, then just 10 seconds after that McAllister's goal-bound header was palmed away brilliantly by Stanley keeper Kenny Arthur.
Accrington went closest in the early stages of the second half. John Coleman's side saw Andy Proctor and Michael Symes, on his Stanley debut, both see shots blocked in quick succession, then Proctor found plenty of space in the Exeter box, but he blazed over.
Stanley made no mistakes on 62 minutes though. Chris Turner crossed from the right, and Craig Lindfield was allowed far too much space as he prodded the ball home from eight yards.
Turner fluffed a great chance to increase the hosts' lead when he volleyed tamely at Jones, then Cavanagh came close when his cross-cum-shot floated inches past the far post.
Dean Moxey smashed a disappointing shot wide for Exeter in stoppage time.