The Latics were 3-0 up and in total control at half-time after goals from Aidan White, Oumare Tounkara and Chris Taylor.
Exeter launched their fightback in the 77th minute when Richard Logan fired home, and Jamie Cureton and Daniel Nardiello then struck to haul Tisdale`s team level.
City even missed a penalty after 88 minutes as Dean Brill tipped Ryan Harley's spot-kick onto the post after Carl Winchester tripped Nardiello
"Obviously we are delighted. It has been a long few days playing at Huddersfield on Saturday and here but four points from two games is fantastic," said Tisdale. "As soon as we got one goal back, even without much time left, I thought we could get something.
"We didn't adapt in the first half when Oldham looked a very dynamic team and definitely deserved their lead. But we got some structure and the substitutions made a difference. We got the impetus in our favour and the players deserve great credit for that."
Source: PA
Source: PA