Mark Hughes was sacked by Stoke City on Saturday night after he watched his side get dumped out of the FA Cup at Coventry City.
Stoke were downed 2-1 by the Sky Blues after Jack Grimmer's 68th-minute effort put Coventry ahead following Charlie Adam's leveller from the penalty spot.
The Potters tweeted out the announcement on Saturday evening, and said they "will look to appoint a new manager as soon as possible."
Elsewhere, Manchester City recvovered from Ashley Barnes' early opener to beat Burnley 4-1 at the Etihad Stadium.
Guardiola's men took control after goals from Sergio Aguero and one each by Leroy Sane and Bernardo Silva.
In the early game, Fleetwood Town earned a replay at Leicester City after their 0-0 draw, and in the late game Norwich City held Chelsea by the same score at Carrow Road.
Peterbrough earned a stunning win at Aston Villa, with three goals in the final 15 minutes cancelling out Keinan Davis' eighth-minute opener.
On Friday night Manchester United beat Derby County 2-0, and Liverpool beat Merseyside rivals Everton 2-1.
The full list of results is below, with replays to be on the played week commencing January 15 with the fourth-round draw taking place on Monday before Brighton's televised clash with Crystal Palace.
- Fleetwood 0-0 Leicester
- Middlesbrough 2-0 Sunderland
- Aston Villa 1-3 Peterborough
- Birmingham 1-0 Burton
- Bolton 1-2 Huddersfield
- Blackburn 0-1 Hull
- Bournemouth 2-2 Wigan
- Brentford 0-1 Notts County
- Cardiff 0-0 Mansfield
- Carlisle 0-0 Sheffield Wednesday
- Coventry 2-1 Stoke
- Doncaster 0-1 Rochdale
- Exeter 0-2 West Brom
- Fulham 0-1 Southampton
- Ipswich 0-1 Sheffield United
- Man City 4-1 Burnley
- Millwall 4-1 Barnsley
- Newcastle 3-1 Luton
- QPR 0-1 MK Dons
- Stevenage 0-0 Reading
- Watford 3-0 Bristol City
- Wolves 0-0 Swansea
- Wycombe 1-5 Preston
- Yeovil 2-0 Bradford