A goal from Exeter striker Sean Devine in the fifth minute of stoppage time earned his side a precious point in their bid to beat the drop.
After three successive home defeats Orient looked to be heading towards victory when Lee Thorpe fired them ahead on the stroke of half time.
But Exeter refused to give up and from Chris Curran's massive throw Steve Flack knocked the ball down and Devine smashed it home.
A disappointed Orient boss Paul Brush said: "We paid the price for not killing Exeter off.
"We had enough of the ball - it's the second Saturday running we have conceded a late goal which has cost us the win. I'm a cross between annoyed and gutted." But new Exeter boss Gary Peters, who has yet to see his side lose a game, said: "I think we can stay up.
"We mustn't have any fear and our aim has to be to finish as high as possible. It's important we remain positive." In a game where chances were few and far between Exeter went close early on when Flack shot wide and then the dangerous James Coppinger shot tamely at home keeper Glenn Morris.
The visitors also claimed that Flack's 23rd minute header had crossed the line before Orient scrambled it away.
Chris Tate had Orient's first chance in the 36th minute but Grecians keeper Kevin Miller palmed the ball away before Thorpe, looking suspiciously offside, fired Orient ahead just before the interval after Matthew Joseph and Matthew Brazier were involved in the build up.
After the break the wind-assisted O's almost added a second but Miller saved Matthew Lockwood's free kick before Martin Thomas had a goal ruled out for the visitors following a foul on Morris.
Orient's sub Jabo Ibehre missed a great chance in stoppage time to put the issue beyond doubt and they paid the price with Devine's intervention.
But the point was tempered with the news that Coppinger was stretched off with a suspected broken ankle.