Marco Silva's Toffees will head to League One Lincoln City, who won at Championship side Huddersfield in the opening round, while the Hammers will be heading to Wales to take on Newport.
The only all-Premier League tie of the round sees Newcastle take on Leicester, while Leeds's reward for their impressive win at Salford will see them face Stoke at home. Other interesting ties include Norwich heading to Crawley, Aston Villa facing an away day at Crewe, a derby clash between Nottingham Forest and Derby and Sunderland heading to Premier League Burnley. Carabao Cup second round draw, South section: Plymouth v Reading Crawley v Norwich Newport v West Ham Oxford v Millwall Watford v Coventry Swansea v Cambridge Cardiff v Luton Bristol Rovers v Brighton Crystal Palace v Colchester Fulham v Southampton Bournemouth v Forest Green Southend v MK Dons QPR v Portsmouth
North section: Crewe v Aston Villa Lincoln v Everton Leeds v Stoke Sheff Utd v Blackburn Rotherham v Sheff Wed/Bury Newcastle v Leicester Burton v Morecambe Burnley v Sunderland Nottm Forest v Derby Grimsby v Macclesfield Preston v Hull Rochdale v Carlisle Ties to be played week beginning Aug 26.