In other Cup action on Friday, Chelsea eased past Hull City with a 4-0 success.
Wrexham defeated Premier League Nottingham Forest in the last round and dispatched fellow second-tier Championship side Ipswich to reach the fifth round for the first time since they were quarter-finalists in the 1996-97 season.
Josh Windass scored the only goal of the game in the first half as Ipswich battled to create clear-cut chances and Wrexham proved more clinical.
After a tepid start to the game, the home side led on 34 minutes when Max Cleworth's low cross from the right was turned in by Windass for his ninth goal of the season in all competitions.
Ipswich only had one shot on target as Wrexham managed to see out the remainder of the game with relative ease.
North Wales club Wrexham were bought by Hollywood actors Ryan Reynolds and Rob McElhenney in 2020 and have embarked on a rise through the divisions that has attracted global attention.
Chelsea were far too strong for Championship side Hull as they strolled to victory at the MKM Stadium thanks to Pedro Neto's double and a hat-trick of assists from Rory Delap.
After missing several simple chances, they were ahead on 40 minutes with a super strike from Neto. Delap teed him up on the edge of the box and the Portugal international curled his effort into the net.
The visitors doubled their advantage on 51 minutes as Jorrel Hato added a second after getting the slightest of touches to Neto's corner as the ball came through a crowd of players.
Dutch defender Hato also scored in the previous round against Charlton Athletic.
It was 3-0 on 59 minutes when Estevao side-footed into the net from Delap's pass, before Chelsea added a fourth on 71 minutes as Delap again played in Neto for his second.
29°C