Brendan Rodgers' side sealed their place in the fourth round of the famous competition on Sunday thanks to Iago Aspas' first goal for the club and a late James Tarkowski own goal.
Spanish forward Aspas volleyed home in the 54th minute as Liverpool turned the screw after the break, and the same player headed against the post just after.
Oldham - who beat Liverpool 3-2 in the fourth round last year, but lost 5-1 at Anfield in round three in 2012 - weathered the storm though, and almost snatched an equaliser when Michael Petrasso forced an excellent save from Liverpool goalkeeper Brad Jones with 16 minutes left.
|VIEW FROM ANFIELD
|By Tom Maston
Oldham gave an excellent account of themselves, and on another day could have salvaged a replay with some slightly better play in the final third. As it was, though, this was another thoroughly professional job from Brendan Rodgers’ Liverpool.
After huffing and puffing for much of the first half, the emergence of Phillipe Coutinho at half-time gave the hosts much better balance and they certainly deserved their place in the fourth round.
Iago Aspas will gain confidence from finding the net while Raheem Sterling and Jordan Henderson were again impressive for the Reds. Silverware at Anfield this season is certainly a possibility.
Rodgers rested star striker Luis Suarez, midfielder Philippe Coutinho and goalkeeper Simon Mignolet but recalled captain Steven Gerrard for his first start in almost a month.
Jones deputised in goal for Liverpool, while just two members of the Oldham team that beat Liverpool last year - Jonathan Grounds and James Wesolowski - started for Lee Johnson's side.
Gerrard, who returned from a hamstring injury against Hull City on Wednesday, was the victim of a crunching tackle from Oldham captain Korey Smith in the first minute and it set the tone in a frustrating first half for Liverpool.
They rarely threatened the Oldham goal, with Luis Alberto going closest in the 14th minute when he shot just wide after a smart lay-off from Victor Moses.
A poor first half saw Rodgers turn to the bench, as Coutinho and Lucas were introduced in place of Alberto and Moses.
Coutinho swung in two testing corners, the second of which was just headed over by Gerrard, before Aspas broke the deadlock nine minutes after the break.
Raheem Sterling was the provider, causing panic in the Oldham defence with a jinking run, and his ball across the penalty box was allowed to bounce before Aspas volleyed in.
Aspas almost doubled his account two minutes later, but his glancing header from another Sterling cross hit the post, and Coutinho's follow-up was denied by the legs of Oldham goalkeeper Mark Oxley.
Sterling then declined to shoot after charging forward, instead opting to cut back, but Coutinho could only blaze over the bar.
After weathering the storm, Oldham fought back, with Philliskirk again going close from distance before Petrasso span away from Agger and forced a great save from an outstretched Jones.
Rodgers was forced to play his trump card, bringing on Suarez, but it was Sterling who helped wrap up the win, with his strike - that was going wide - going in after an unfortunate Tarkowski deflection.