James Wesolowski and a Liam Ridehalgh own goal twice put Latics ahead but the visitors had to settle for a point from Prenton Park in an entertaining afternoon of football.
Jason Koumas levelled the scores at 1-1 going into the break, whilst Ryan Lowe equalised in the final 15 minutes to ensure that both sides go home with a point.
Latics pressured the home side in the early stages with Gary Harkins and Danny Philliskirk causing a nuisance to the Rovers defenders.
The fans responded to manager Lee Johnson's plea for more songs and they were cheering more when Wesolowski gave Latics the lead after 12 minutes.
The midfielder struck an effort from the edge of the area, wrong-footing goalkeeper, Fon Williams, to put Latics ahead.
With the visitors piling on the pressure, they maybe should have been awarded a penalty ten minutes later.
Philliskirk looked to have been pushed in the area as he raced through on goal but referee, Charles Breakspear waved away the strong Latics' protests.
That decision came to haunt the visitors as Tranmere Rovers found a way back into the game as Koumas brought the scores level.
The winger smashed his effort goalwards from the edge of the area and after a strong deflection off Jonathan Grounds, the ball looped over Mark Oxley and into the back of the goal.
As half time approached, the game turned quite scrappy and both sides would have been happy to go into the break with the scorelines level.
Goalscorer Wesolowski picked up a yellow card early into the first half for Latics after bringing down Andy Robinson as he looked to break.
With the home side attacking, Latics hit Rovers on the counter attack and led for a second time through an own goal.
As the chance looked to be lost, a Rovers defender blasted the ball against Ridehalgh and the ball rolled into the back of the goal to restore the lead.
Latics didn't sit on that lead and went in search of more. Charlie MacDonald played the ball to Philliskirk in space, but the striker missed the target from 18 yards.
With only 15 minutes of the game remaining, Rovers equalised. Jake Cassidy did well on the right-hand side and delivered a cross straight onto the head of Lowe, who powered it past Oxley to level the scores.
Both sides then went in search of a winner as Cassidy was unlucky not to get on the end of a teasing cross, whilst at the other end, David Worrall's header smashed against the side netting.
After a nervy ending where Latics had to withstand pressure from a succession of deep throw-ins, they held on for a point to take back to Boundary Park.
Tranmere Rovers: Fon Williams, Holmes, Taylor, Wallace, Lowe, Robinson (Rowe 89'), Cassidy, Jennings, Koumas (Kirby 70'), Ridehalgh, Arthurworrey.
Subs Not Used: Horwood, Goodison, Stockton, Power, Mooney.
Oldham Athletic: Oxley; Brown, Lockwood, Grounds, Mellor; Worrall, Wesolowski, Smith, Harkins; Philliskirk, MacDonald (Clarke Harris 84').
Subs Not Used: Rachubka, Winchester, Dayton, Dunfield, Stead, Clarke
Goals: Tranmere Rovers (Koumas 30', Lowe 75') 2-2 Oldham Athletic (Wesolowski 12', Ridehalgh OG 58')
Attendance: 5,061 (757 Visiting Supporters)