Everton will host Championship side Rotherham United in the second round of the 2018-19 EFL Cup.
The Toffees have never won the competition before, but will begin their quest to change that statistic under Marco Silva when Rotherham visit Goodison Park later this month.
Elsewhere in the northern section of the draw, Leicester City were paired with Fleetwood Town, giving striker Jamie Vardy the chance to face one of his former clubs.
The only all-Premier League affair in either section was the first out of the hat, with Brighton & Hove Albion hosting Southampton at the Amex Stadium.
There are also home ties for Fulham and Cardiff City, but fellow newly-promoted side Wolverhampton Wanderers will face an away trip to face either Sunderland or Sheffield Wednesday.
West Ham United are also on the road against AFC Wimbledon, while Crystal Palace take on Swansea City at the Liberty Stadium, Huddersfield Town visit Stoke City and Bournemouth host MK Dons at the Vitality.
EFL CUP SECOND ROUND DRAW IN FULL
Southern section
Brighton vs. Southampton QPR vs. Bristol Rovers Wimbledon vs. West Ham Fulham vs. Exeter City Wycombe Wanderers vs. Forest Green Rovers Cardiff vs. Norwich Millwall vs. Plymouth Argyle Brentford vs. Cheltenham Town Swansea vs. Crystal Palace Newport County vs. Oxford United Bournemouth vs. MK Dons Reading vs. Watford
Northern section
Leicester vs. Fleetwood Town Leeds vs. Preston Sunderland or Sheff Wed vs. Wolves Nottingham Forest vs. Newcastle Doncaster Rovers vs. Blackpool Burton vs. Aston Villa Hull vs. Derby Middlesbrough vs. Rochdale Everton vs. Rotherham Blackburn vs. Lincoln City West Brom vs. Mansfield Walsall vs. Macclesfield Stoke vs. Huddersfield