Reds captain Steven Gerrard put more than two months of frustration behind him to score on his first start since October as Oldham were brushed aside.
After three substitute appearances following recovery from an ankle infection the 31-year-old finally reclaimed his place in the team and expertly dispatched the penalty which put his side into a lead they did not surrender despite a valiant effort from their League One opponents.
Gerrard did the same thing back in October when, on his first start after six months out after a groin operation, he scored against Manchester United.
On that occasion he played only one more match before succumbing to the ankle problem which sidelined him until Boxing Day.
The England international will be hoping recent history does not repeat itself as Liverpool have an important few months ahead of them, starting with a two-legged Carling Cup semi-final against Manchester City next week.
Almost exactly a year ago manager Kenny Dalglish marked the start of his second spell in charge at the club with a third-round exit at Manchester United 24 hours after replacing Roy Hodgson.
There was no recurrence against a side 52 places below them in the league - although for a fleeting moment the visitors threatened a shock with a brilliantly-taken goal from Robbie Simpson which would not have looked out of place had it been scored at Wembley itself.
A week ago the 26-year-old Simpson was not even registered to play for the Latics but he re-signed on loan from Huddersfield less than a week ago and his 30-yard strike will have done no harm in securing him a permanent move.
If the Latics had held on for longer than two minutes they may have stood a chance but a freakish deflected equaliser via Craig Bellamy and Gerrard's penalty put the Reds in control and Jonjo Shelvey's first goal for the club and late efforts from substitutes Andy Carroll and Stewart Downing wrapped things up.
With Gary Ablett's family watching from the stand there was a minute's applause for the former Liverpool defender who died on New Year's Day aged 46 after losing a 16-month battle with non-Hodgkin's lymphoma.
The Reds may be unbeaten at home this season but they have often struggled at Anfield and they were fortunate not to go behind after just 10 minutes.
Experienced striker Shefki Kuqi outmuscled Sebastian Coates and wrong-footed Jamie Carragher but wastefully shot into the side-netting with only Jose Reina to beat.
Right-back Tom Adeyemi had an equally good chance from Simpson's 14th-minute corner but planted his free header just over while Chris Taylor also fired wide.
Oldham deservedly took the lead in spectacular style in the 28th minute when, after receiving Dean Furman's pass, Simpson took one touch before unleashing a left-footed half-volley which flew past Reina.
The goal had the Oldham contingent in the directors' box - and the 6,132 visiting fans - on their feet but they were soon pegged back by a huge stroke of luck.
Shelvey cut in from the right and speculatively aimed for the far post only for the shot to take a huge deflection off Bellamy's chest and leave Alex Cisak helpless.
Gerrard put his side ahead just before the interval when, after Maxi Rodriguez was pushed by Adeyemi, he expertly converted only the second of six penalties the Reds have been awarded this season.
Bellamy, Dirk Kuyt and Martin Kelly all had chances early in the second half - the latter brilliantly denied by Cisak - before Shelvey smashed home from Bellamy's 68th-minute cross.
Late in the second half Adeyemi appeared to take offence to something shouted from the Kop and despite reassurance from his team-mates, Kuyt and Gerrard, the 20-year-old right-back, on loan from Norwich, seemed visibly upset.
There then appeared to be discussion between the fourth official and a police officer down by the tunnel.
In the 89th minute Carroll smashed in a low shot from outside the area barely two minutes after coming on before Downing, also coming off the bench, wrapped things up even later.