Without being brilliant, the Reds took the lead thanks to a long shot from Harvey Elliott's left which lobbed José Sa in the 13th minute and then held on.
In the round of 16, the defending champion will have an even tougher match since he will go on January 29 to face Brighton, a team which has just beaten him 3-0 in the league last Saturday.
In the other matches of the evening, the logic was respected, and the dream stopped for Chesterfield, one of the three 5th division clubs still in contention.
While leading 3-2 in the 92nd minute of the first match, Petit Poucet had seen West Bromwich Albion come back to 3-3 and could not do anything on the lawn of the D2 club (4-0) on Tuesday evening .
On Wednesday, Boreham Wood, another D5 club, will go to Accrington (D3) to try to imitate Wrexham who had achieved (4-3) the feat at Convetry (D2).
Another Premier League team, Leeds, will also have a chance to join the 16th, receiving Cardiff City (D2).
In the first game, in Wales, Leeds, trailing 2-0, managed to equalize 2-2 in added time.
Result of the 32nd finals:
Tuesday
1st game:
Forest Green Rovers (D3) - Birmingham (D2) 1 - 2
Matches to replay:
West Brom (D2) - Chesterfield (D5) 4 - 0
Wigan (D2) - Luton Town (D2) 1 - 2
Wolverhampton - Liverpool 0 - 1
Swansea (D2) - Bristol Rovers (D2) 1 - 2
Wednesday
Accrington Stanley (D3) - Boreham Wood (D5)
Leeds United - Cardiff City (D2)
© 2023 AFP