Josh Benson’s late strike secured a 1-0 win for the Tykes at The Riverside and they will head to Elland Road next, while Everton travel to League One Fleetwood Town, Newcastle head to Tranmere and Aston Villa take on Bolton.
Elsewhere, there are also testing away trips to League Two sides for newly-promoted Nottingham Forest, who face Grimsby Town, and Fulham, who go to Crawley Town.
Southampton will visit Cambridge United, Brentford go to Colchester United, while Oxford United host Crystal Palace and Forest Green Rovers welcome Brighton.
Fleetwood Town v Everton
Grimsby Town v Nottingham Forest
Crawley Town v Fulham