Carabao Cup holders Liverpool will begin the defence of their crown at home to West Ham in the third round as a seeding system was introduced in the competition for the first time.
The six English sides taking part in the Champions League and Europa League were all seeded in the draw, meaning they would not have to face each other at this stage.
Arsenal were drawn at home to League One side Bolton Wanderers, with Manchester United welcoming Barnsley to Old Trafford.
Reigning Premier League champions Manchester City will take on Championship Watford at Etihad Stadium, while Aston Villa and Tottenham have been handed trips to Wycombe and Coventry respectively.
League Two side Barrow’s reward for reaching the third round for the first time since 1967-68 is a trip to beaten 2024 finalists Chelsea, while AFC Wimbledon – who defeated Premier League Ipswich on penalties in the second round – will host Newcastle.
There are three all-Premier League encounters, as Everton face Southampton at Goodison Park and Brighton host Wolves at the Amex Stadium.
The changes to this year’s third-round draw were brought in following the expansion of the Champions League and Europa League, which will see clubs play a minimum of two extra matches.
Ties will take place in the weeks commencing 16 and 23 September, with Champions League and Europa League fixtures also scheduled during this period.