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
Barney Corkhill
