The Reds fell to Oldham in the FA Cup last year, but avoided a repeat at Anfield. The Reds were not at their best in the first half, as they failed to truly test Mark Oxley in the opening 45 minutes.
The best chance of the opening stanza fell to Luis Alberto, but he shot straight at the keeper.
Reds boss Brendan Rodgers made changes at the break, as he threw on Lucas and Philippe Coutinho.
The latter was an influence from the off. He whipped in a dangerous cross that Steven Gerrard met with a thumping header, but was unable to keep it down.
The breakthrough came on 54 minutes, with Iago Aspas turning home Raheem Sterling’s cross for his first goal with the club.
Aspas went within a whisker of doubling his Liverpool tally a couple of minutes later, but his header crashed against the post.
The Reds made the game safe on 82 minutes, as a shot from Sterling was deflected beyond Oxley off the unfortunate James Tarkowski.
That goal eased the nerves, as Liverpool had to play the final 10 minutes with 10 men. Daniel Agger was forced off with an injury after Rodgers had made his three substitutions.
Looks like Liverpool's injury problems could be set to worsen after Agger went down clutching his calf.— Tony Barrett (@TonyBarretTimes) January 5, 2014
Luis Suarez started the game on the bench, but came on with 15 minutes remaining. The free-scoring forward did not get a sight of goal and it was a rare blank shooting day for the Uruguayan.
It was only a cameo appearance of course, but today was only the 2nd time in 113 #LFC appearances that Suárez didn't have a shot— Andrew Beasley (@BassTunedToRed) January 5, 2014
Philippe Coutinho: B+
The midfielder may have only played the second half, but he demonstrated his importance to the club in those 45 minutes. He was a composed figure in the middle of the park, his passing was assured and he created chances.
Iago Aspas: B
Aspas has not made a huge impression since joining the Reds from Celta Vigo in the summer, but the tide may now be turning. He looked a threat and got a goal his overall display merited.
Yes, he was only facing League One opposition, but forwards thrive on confidence and nothing breeds confidence quite like goals.
Liverpool lead against Oldham through Iago Aspas' first competitive goal for the club. pic.twitter.com/qlmxHVOI5E— Squawka Football (@Squawka) January 5, 2014
Victor Moses: D
The Chelsea loanee was handed a chance to shine by manager Brendan Rodgers, but was unable to make much of an impression. A disappointing display was cut short when Rodgers withdrew him at the interval.