Everton loan man Jose Baxter's first-half strike was enough to give Tranmere all three points against Oldham.
Baxter's shot from Lucas Akins' pass took a deflection off Rovers centre forward Enoch Showumni to beat visiting keeper Alex Cisak.
Adam McGurk came close to doubling the advantage but his header from an Akins cross came back off the crossbar.
Latics striker Shefki Kuqi fired wide from distance as the hosts comfortably held out.
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Tranmere manager Les Parry told BBC Radio Merseyside:
"Ian Goodison and Ash Taylor were fantastic as (Oldham) are a handful and we thought both of them were superb.
"We don't want to have to score three goals to win a game and at the moment we're keeping clean sheets and we've kept more clean sheets than anyone in this division.
"We were looking to get six points from our two home games and we've got three of them so at least we're half way there."
Oldham manager Paul Dickov told BBC Radio Manchester:
"What our players have got to realise is they can't just turn up at football matches and start the way they did today.
"Every time you play football you have to go out there and have desire and, I think, mentally after a couple of wins they switched off.
"It tells me they get complacent. It tells me they don't retain the information we give them and I'm getting a bit sick of it."