Manchester City has kept their extended their unbeaten run under Pep Guardiola to nine matches following a 2-1 win at Swansea on Thursday morning (AEST) in the EFL Cup.
Gael Clichy and Aleix Garcia scored for the visitors, as Gylfi Sigurdsson grabbed a goal in stoppage-time, although it would be too late for the Swans.
Their Manchester rivals also progressed through to the fourth round, after United beat Northampton Town 3-1.
Michael Carrick opened the scoring before a penalty brought Northampton level at half-time, but second half goals to Ander Herrera and Marcus Rashford was enough for United to advance.
Tottenham put five past Gillingham at White Hart Lane and Southampton saw off Crystal Palace, as most results went as planned on an eight-game day.
West Ham left it late against League Two side Accrington however, and needed star man Dimitri Payet to bail them out in the 96th minute with a free kick to send the Hammers through on a 1-0 win.
Fulham 1 (Piazon 14) Bristol City 2 (Wilbraham 45, Abraham 90)
Northampton 1 (Revell 42-pen) Manchester United 3 (Carrick 17, Herrera 68, Rashford 75)
QPR 1 (Sandro 60) Sunderland 2 (McNair 70, 80)
Southampton 2 (Austin 33-pen, Hesketh 63) Crystal Palace 0
Stoke 1 (Arnautovic 24) Hull 2 (Mason 45, Henriksen 90+1)
Manchester City 2 (Clichy 49, Garcia 67) Swansea 1 (Sigurdsson 90+3)
Tottenham 5 (Eriksen 31, 48, Janssen 51-pen, Onomah 65, Lamela 68) Gillingham 0
West Ham 1 (Payet 90+6) Accrington 0