United, who beat Aston Villa in the Wembley final in February, will make the trip to Glanford Park to face Nigel Adkins' Championship side - who beat Sheffield Wednesday in the second round.
Northampton, the only League Two side surviving in the competition, were handed a dream trip to Anfield to take on Liverpool.
Villa take on Blackburn, while Newcastle face a daunting trip to London to take on free-scoring Chelsea.
Manchester City head to West Brom in another all-Premier League clash, while Stoke meet Fulham and Sunderland will have home advantage against West Ham.
Burnley, relegated from the Premier League last season, will relish their clash against top-flight neighbours Bolton, and League One Brentford have an attractive home match against Everton.
Notts County's reward for knocking out Watford is a trip to Wolves, while MK Dons - who stunned Blackpool in the second round - face more Premier League opposition with a short journey to play Birmingham at St Andrew's.
There is another north-west clash between Wigan and Preston, while elsewhere Portsmouth will tackle Leicester at Fratton Park, Peterborough face Swansea and Millwall will play Ipswich.
Draw for Carling Cup third round:
Brentford v Everton
Portsmouth v Leicester
Stoke v Fulham
Chelsea v Newcastle
Aston Villa v Blackburn
Tottenham v Arsenal
Millwall v Ipswich
Wolverhampton v Notts County
Burnley v Bolton
Birmingham v MIK Dons
Liverpool v Northampton
Scunthorpe v Man Utd
West Brom v Man City
Sunderland v West Ham
Peterborough v Swansea
Wigan v Preston
Ties to be played week of Sept 20