The Hertfordshire side overcame their Championship opponents at the Keepmoat Stadium and will now host Roberto Martinez's men, who have impressed in the Premier League so far this season.
The Premier League big boys have all been kept apart with Arsenal, who beat north London rivals Tottenham at the Emirates Stadium on Saturday evening, at home again against cash-strapped Coventry.
Chelsea will host Stoke after beating Derby on Sunday, with the winner of the Manchester City v Blackburn replay facing a home fixture against Bristol City or Watford.
Rochdale's reward for beating Leeds in the third round is a fourth-round meeting at home to either Macclesfield or Sheffield Wednesday.
Keith Hill's Sky Bet League Two side recorded a deserved 2-0 win over the 1972 winners and will be hopeful of progression in to round five as they welcome either cash-strapped Macclesfield or three-time winners Wednesday.
FA Cup 4th round draw:
Sunderland v Kidderminster or Peterborough
Bolton v Cardiff
Southampton v Yeovil
Huddersfield v Charlton or Oxford
Port Vale or Plymouth v Brighton
Nottingham Forest v Ipswich or Preston
Southend v Hull
Rochdale v Macclesfield or Sheffield Wednesday
Arsenal v Coventry
Stevenage v Everton
Wigan or MK Dons v Crystal Palace
Chelsea v Stoke
Blackburn or Manchester City v Bristol City or Watford
Bournemouth or Burton v Liverpool
Birmingham, Bristol Rovers or Crawley v Swansea
Sheffield United v Norwich or Fulham
Ties to be played on the weekend of January 25 and 26.