Seven of the nine Premier League teams in EFL competition on Tuesday night won their ties.
Antonio Conte's Chelsea were made to sweat by League OneBristol Rovers, and brought on Eden Hazard and John Terry from the bench, but went through at Stamford Bridge courtesy of a 3-2 win in which new signing Michy Batshuayi scored twice, while Adama Diomande claimed a double as Hull came from behind to beat Exeter 3-1.
Former England striker Peter Crouch bagged a hat-trick, completing his treble with an acrobatic scissor kick, in his first appearance of the season as Stoke defeated Stevenage 4-0 and his old club Liverpool also progressed courtesy of a 5-0 rout of Burton, with Daniel Sturridge claiming the fourth and fifth goals.
Swansea, winners of this competition in 2013, beat Peterborough 3-1, Crystal Palace were 2-0 winners over Blackpool on a night when £27million signing Christian Benteke played 45 minutes on his debut and Everton recorded a 4-0 triumph over Yeovil at Goodison Park.