England international Carroll, bought for 35 million pounds from Newcastle United last January, pounced with injury-time approaching to put Liverpool 4-1 up after they had gone behind in the 28th minute.
Oldham's Robbie Simpson produced an unstoppable strike from 25 metres in the 28th minute but Liverpool quickly drew level when a Jonjo Shelvey shot destined for the goalkeeper's hands deflected off Craig Bellamy into the corner of the net.
Liverpool captain Steven Gerrard, plagued by injuries in 2011, then rifled home a penalty at the end of the first half to give his side a 2-1 lead.
Bellamy's pace unsettled Oldham as Liverpool made it 3-1 after 68 minutes, the Welsh winger's cross after a dashing run dispatched by Shelvey.
Misfiring striker Carroll then grabbed his third goal of the season after a swivel on the edge of the box and a smart finish before Stewart Downing made it 5-1 deep into injury-time.
SOUR NOTE
"Downing scored, big Andy got a goal, Jonjo scored and Steven scored with a penalty so we've had a few positives but I don't think the scoreline reflects the distance between the two teams on that performance," said Liverpool boss Kenny dalglish.
However, the game ended on a sour note when Oldham's Tom Adeyemi exchanged words with a spectator and the tearful midfielder needed a consoling word from Gerrard.
Liverpool issued a statement saying: "An incident occurred in the second half of the match which is now being investigated by both the club and the police."
Merseyside Police added: "The aim of the investigation is to establish the full circumstances surrounding the incident to ascertain if action needs to be taken."
"[We] can confirm that no-one has been arrested this evening... on suspicion of racially aggravated behaviour during tonight's FA Cup fixture at Anfield," said a police spokesman.
