A first Liverpool goal for Iago Aspas helped the Reds to a hard-fought 2-0 win over Oldham in the third FA Cup meeting between the two sides in as many seasons.
Liverpool atoned for their Fourth Round defeat at Boundary Park last season but were pushed hard by the stubborn League One team.
The seven-times FA Cup winners had to bide their time for a breakthrough and Aspas broke the deadlock on 54 minutes, much to the relief of the Anfield crowd.
FA Cup Fourth Round draw
(selected ties)
Bournemouth or Burton v Liverpool
Sunderland v Kidderminster or Peterborough
Port Vale or Plymouth v Brighton
The Spaniard collected the ball at the back post from the impressive Raheem Sterling and placed his shot across goalkeeper Mark Oxley into the corner of the net.
Although one goal looked to be enough to confirm Liverpool's progress in the FA Cup, the hosts had goalkeeper Brad Jones to thank after he denied Oldham's Micheal Petrasso with a smart low save.
Liverpool doubled their lead on 82 minutes when Sterling's shot deflected off of James Tarkowski and bounced into the Oldham net.
FA Cup highlights from Anfield.
Brendan Rodgers' side will travel to either Bournemouth or Burton Albion in the Fourth Round.
Elsewhere, two-time FA Cup winners Sunderland earned a Fourth Round home tie against either Kidderminster Harriers or Peterborough United after a resilient 3-1 victory over Carlisle United at the Stadium of Light.
Adam Johnson's sublime free-kick put the home side ahead on 36 minutes in the first meeting between the two sides in the FA Cup since 1995.
The 26-year-old beat Cumbrians' goalkeeper Greg Fleming by curling his effort into the top left-hand corner.
The Premier League team did not have it all their own way in the first half as their League One opponents rallied despite difficult playing conditions on Wearside.
Midfielder Matt Robson equalised for the visitors just before the half-time break with an instinctive finish in the penalty area.
He was alert to pounce quickly and stab the ball home off the underside of the crossbar after Lewis Guy's initial knock down.
It did not take Sunderland long to restore their lead and it was positive attacking play from Johnson again which made the difference.
The winger volleyed a cross-field pass from Ondrej Celustka goalwards and Carlisle's Sean O'Hanlon unluckily diverted the ball over Fleming and into his own net.
Graham Kavanagh's team piled forward in search of an equalising goal but Black Cats debutant El-Hadji Ba made it 3-1 following clever link-up play with Jozy Altidore.
Sunderland manager Gus Poyet said afterwards: "We are going to become a Cup team. It was a professional performance today. We needed to do the job.
Video highlights from the Stadium of Light.
"It's never easy. You need to cope with a few situations and a few shots, but in the end, you need to be better, so job done."
Kavanagh, meanwhile, was brimming with pride at his team's Cup performance: "It's huge. It's so exciting for a club like ourselves to come to a stadium as big as this with a fan-base as big as it is.
"For us then to get behind it because of the location and go and support the game and the team as they have done, and then always to feel that you have that chance of potentially going through and looking to see who you are going to draw.
"When we beat Brentford and the draw was made for Sunderland, the excitement around the city was huge."
Kavanagh added: "The romance of the cup has always been, and will always be fantastic."
Meanwhile, League Two side Plymouth produced a superb fightback from two goals down to earn an FA Cup Third Round replay against Port Vale.
Second half goals from Reuben Reid and Ben Purrington levelled the match at two apiece.
The winner of the replay at Home Park will meet Brighton in the Fourth Round.
Port Vale made their home advantage count in the first half and deservedly led 2-0.
Gavin Tomlin’s header on 15 minutes put Micky Adams’ League One charges in control and striker Tom Pope doubled their lead on 36 minutes with an instinctive finish.
In the second period, John Sheridan's Plymouth side began with renewed purpose and were rewarded on 51 minutes.
Reid combined nicely with Lewis Alessandra before calmly slotting the ball past goalkeeper Chris Neal to reduce the deficit.
With just over 15 minutes to go, Port Vale failed to clear their lines and Alessandra picked up the ball in a dangerous position before feeding the run of Purrington, who in turn exquisitely clipped his effort into the net.
