Goalkeeper Viktor Johansson was the hero as Stoke started life after Steven Schumacher with a 2-1 penalty shoot-out victory over Fleetwood.
Ange Postecoglou has hit back at criticism over his own claim that he "always wins things" in his second year, saying it is true and he plans to do it again.
Sando Tonali made an impressive return from his 10-month betting ban as Newcastle knocked Nottingham Forest out of the Carabao Cup on penalties.
Liverpool will begin their defence of the Carabao Cup with the visit of West Ham to Anfield next month.
Hakon Valdimarsson was the hero for Brentford after his 82nd-minute penalty save earned them a 1-0 Carabao Cup win at Colchester.
Jarrod Bowen's late strike put West Ham into the Carabao Cup third round after a 1-0 win over Bournemouth.
Wycombe shocked Championship side Swansea in the Carabao Cup as a first-half strike from Richard Kone earned the visitors a 1-0 win in the second round.
Two late goals from James Bree and Cameron Archer earned Southampton a Carabao Cup win over Cardiff.
Goalkeeper Owen Goodman was AFC Wimbledon’s hero as the League Two side knocked Premier League Ipswich out of the Carabao Cup on penalties.
Goncalo Guedes struck twice to seal Wolves' spot in the third round of the Carabao Cup with a 2-0 win over Burnley.
Watch all the goals from the second round of the Carabao Cup.
Brighton booked their place in the third round of the Carabao Cup with a 4-0 home victory over League One Crawley.
Jay Stansfield refused to celebrate his goal on his return to Birmingham as Fulham cruised to a 2-0 Carabao Cup second-round win.
Jean-Philippe Mateta struck twice at Selhurst Park to inspire Crystal Palace to a 4-0 Carabao Cup second-round victory over Norwich.
Everton finally gave their fans something to smile about with a comprehensive 3-0 victory against Doncaster in the Carabao Cup.
League Two side Barrow ended their 56-year wait for a place in the Carabao Cup third round by beating Championship side Derby 3-2 on penalties after the tie finished 0-0.
Leicester secured safe passage through to the third round of the Carabao Cup with a dominant 4-0 victory over Tranmere.
Watch any Carabao Cup match this season on Sky Sports+, with the second round coming to a close on Wednesday - and the televised third round draw following afterwards.
Watch highlights from all of Tuesday night's Carabao Cup second-round ties here...
The Carabao Cup second-round fixture dates have been announced, with every game live on Sky Sports.