Goals from Nathan Dyer, Gylfi Sigurdsson and Marvin Emnes comfortably saw them through to the fourth round at Liberty Stadium.
Marc Muniesa proved the unlikely hero as Stoke came from behind to record a 2-1 victory at Sunderland.
The full-back, who never before scored for Stoke, struck twice to dump last season’s finalists out. Jozy Altidore gave Sunderland a 16th-minute lead.
Goals from Johnny Russell and an own goal by Ireland’s Alex Pearce saw Derby beat Reading 2-0.
James Collins’s goal saw Shrewsbury upset Norwich.
A brace from Dan Gosling and a Charlie Daniels goal saw Bournemouth thump Cardiff 3-0 and add to the Bluebirds woes.
MK Dons, Manchester United’s conquerors in the previous round, saw off Bradford with two more goals form Benik Afobe.
Sheffield United got the better of fellow League One side Leyton Orient, Michael Higdon securing a 1-0 victory at Brisbane Road.
Fulham saw off Doncaster 2-1 with goals from Bryan Ruiz and Daniel Burn. James Coppinger scored Doncaster’s goal.