Newcastle have also made it through to the fourth round
Liverpool are through to the fourth round of the FA Cup after beating Plymouth Argyle 1-0 in their third round replay.
Brazilian holding midfielder Lucas Leiva scored his first goal since 2010 on 18 minutes to put the Premier League side 1-0, heading in a Philippe Coutinho corner.
The Reds could have made the scoreline a little bit more comfortable late on, but Belgian striker Divock Origi missed a late penalty as goalkeeper Luke McCormick made the save to deny him.
League Two Plymouth will be proud of their efforts, having earned a 0-0 draw at Anfield to force a second string Liverpool side into a replay on the south coast.
Reds manager Jurgen Klopp did not strengthen significantly for the replay but did field Coutinho, who is working his way back to full match fitness after injury, as well as Daniel Sturridge.
Liverpool's reward for advancing to the fourth round is a tie against the Championship's Wolverhampton Wanderers at Anfield.
Plymouth Argyle's Luke McCormick (left) saves a penalty from Liverpool's Divock Origi (right) during the Emirates FA Cup, third round replay match at Home Park, Plymouth. Picture by Andrew Matthews PA Wire/PA Images
Elswhere, Southampton struck late to edge past second tier Norwich City with Ireland striker Shane Long finding the net in the second minute of stoppage time to give the Saints a 1-0 win.
Long's Ireland team-mate Robbie Brady started for the Canaries.
Southampton will now face Arsenal at St Mary's in the fourth round.
Rafa Benitez's Newcastle United also made it through at the second attempt as they defeated fellow Championship side Birmingham City 3-1 at St James Park in their third round replay.
Matt Ritchie scored twice for the Magpies either side of a Yoan Gouffran effort.
David Cotterill scored Birmingham's goal before Ritchie netted his second.
Newcastle will now face League One Oxford United in the fourth round.