Saints dominated the first half of Saturday's League One encounter and, after Rickie Lambert had seen a shot well blocked by Rob Edwards, grabbed a fully deserved lead.
Richard Duffy failed to deal with a free-kick at the back post and Adam Lallana was on hand to fire the visitors ahead.
The Grecians had failed to manage a single shot on goal in the first half but equalised four minutes after the restart.
Scott Golbourne delivered a corner to the far post where captain Matt Taylor was on hand to power a header past Kelvin Davies.
Exeter hit a post in stoppage time through substitute Bertie Cozic, before former Exeter defender Danny Seaborne poked a shot over the bar for Saints with the last kick of the game.