Liverpool will face their former assistant manager Steve Clarke again as they kick off their Capital One Cup defence with a trip to West Brom.
Clarke, who was Kenny Dalglish's assistant at Anfield before both men were sacked in the summer, took charge at The Hawthorns in June.
He led Albion to a 3-0 Premier League win over Liverpool on the opening day.
Manchester United host Newcastle, neighbours City are at home to Aston Villa and Chelsea face Wolves.
Tottenham, still looking for their first win under new manager Andre Villas-Boas, face an awkward trip to League One Carlisle, who put out Championship side Ipswich in the last round.
Other intriguing ties see Everton, winners of their opening three league and cup games, visit Neil Warnock's Leeds, and Sunderland travel to League One side MK Dons, conquerors of Blackburn in round two.
Paolo di Canio's Swindon, who caused an upset by knocking out Premier League Stoke in the last round, have been handed a home tie against Championship side Burnley.
Crawley will be at home to Swansea and Arsenal host Coventry, while QPR face Reading in an all-Premier League match-up.
The ties will be played on the week commencing 24 September.
Capital One Cup third round draw:
Man Utd v Newcastle
Man City v Aston Villa
MK Dons v Sunderland
West Brom v Liverpool
Crawley v Swansea
QPR v Reading
Norwich v Doncaster
Bradford v Burton
Preston v Middlesbrough
Arsenal v Coventry
Southampton v Sheff Wed
Chelsea v Wolves
Carlisle v Tottenham
Swindon v Burnley
West Ham v Wigan
Leeds v Everton