The Latics looked to be cruising when they went 2-0 up in the first 30 minutes but both sides were much stronger going forward than they were in defence.
City kept fighting back right up to injury time when Scott Murray ended the scoring in a highly entertaining match.
But Oldham deserved the win and had the two most influential players on the pitch in midfield pair Mark Hughes and Richie Wellens.
Hughes opened his Oldham account with a goal after four minutes which he smashed in from 10 yards following a cross by David Eyres.
The tone was set moments later when City went down to the other end and Murray hit the bar with a header at the far post.
Murray missed another chance to equalise when he was denied by keeper Chris Day and Oldham took advantage on 25 minutes.
Eyres fed Wellens inside the box and the former Manchester United and Blackpool player cut inside from the left before shooting into the far corner from 10 yards.
City pulled one back shortly after half time as Oldham lost possession outside their own box and James Quinn set up Scott Brown for a brilliant volley into the roof of the net from 18 yards.
Oldham regained their two-goal lead thanks to Chris Porter who rose at the near post to head in from eight yards.
Bristol's second goal came from Quinn, the Northern Ireland international striker who has just signed on loan from Peterborough.
His first effort was blocked by Day but Quinn seized on the rebound to score from 12 yards.
Captain Andy Liddell made it 4-2 on 87 minutes after going clean through and picking his spot in the bottom corner.
Murray's superb chip from the edge of the box in stoppage time proved to be the final consolation for the visitors.