Holders Manchester United will begin their defence of the EFL Cup with a home tie against Championship club Burton Albion at Old Trafford.
Thursday's third-round draw in Beijing, which took place at 04:15 BST, also saw Liverpool drawn away to Premier League rivals Leicester.
Manchester City go to West Brom, while Arsenal will host League One Doncaster Rovers.
Nottingham Forest's reward for beating Newcastle is a trip to Chelsea.
The 16 fixtures will be played in the week commencing 18 September.
It will be Burton's first trip to Old Trafford for 11 years. In 2006, as a non-League club, they earned a lucrative FA Cup third-round replay after holding a United team featuring players such as Cristiano Ronaldo and Wayne Rooney to a goalless draw.
There are four all-Premier League ties in total, with Crystal Palace hosting Huddersfield and Brighton travelling to Bournemouth.
The winners of the delayed second-round tie between Championship Barnsley and Derby County face a trip to Wembley after being drawn away to Tottenham.
Bristol Rovers, 18th in League One and the lowest-ranked club left in this season's competition, visit Championship Wolves, who knocked out last season's runners-up Southampton on Wednesday.
Burnley's new club record £15m signing Chris Wood faces an early reunion with his former Leeds United team-mates at Turf Moor.
Third time lucky
There was surprise when the organisers announced earlier in the week the draw would be taking place in China at 04:15 BST on Thursday.
Previous draws for the competition have suffered problems - including teams being drawn out twice and confusion around home and away ties.
The third-round draw appeared to go without incident. There was no live coverage of the draw - on television or online - but details were released on social media.
This is the first season of a three-year naming rights deal for the EFL Cup - formerly the League Cup - with Carabao, a Thai energy drink.
Third round draw
West Bromwich Albion v Manchester City
Everton v Sunderland
Leicester City v Liverpool
Manchester United v Burton Albion
Brentford v Norwich City
Wolverhampton Wanderers v Bristol Rovers
Burnley v Leeds
Arsenal v Doncaster Rovers
Bristol City v Stoke City
Reading v Swansea City
Aston Villa v Middlesbrough
Chelsea v Nottingham Forest
West Ham United v Bolton Wanderers
Crystal Palace v Huddersfield Town
Tottenham Hotspur v Barnsley/Derby County
Bournemouth v Brighton and Hove Albion