Watford and West Brom were the Premier League casualties on a night when most of the top-flight sides made light work of their EFL Cup second-round ties.
Seven of the nine Premier League teams in action advanced in normal time but Watford were beaten at home in extra-time by Gillingham, while West Brom lost 4-3 on penalties to another League One side in Northampton.
Earlier, Antonio Conte's Chelsea were made to sweat by League One Bristol Rovers, but went through at Stamford Bridge courtesy of a 3-2 win in which new signing Michy Batshuayi scored twice.
The Blues twice held two-goal leads but though Rovers had several chances to equalise after Ellis Harrison dragged the visitors back to 3-2, Eden Hazard and Oscar came on to reinforce Chelsea and the visitors eventually ran out of steam.
Liverpool made much lighter work of lower-league opposition, thrashing Burton Albion 5-0 at the Pirelli Stadium and several of their rivals followed suit.
The impressive Sadio Mane teed up Divock Origi for the Reds' opener on 15 minutes and after Roberto Firmino and a Tom Naylor own goal extended the Reds' lead, a late double by substitute Daniel Sturridge added further gloss.
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, while Arouna Kone struck twice as Everton romped to a 4-0 win of their own over Yeovil at Goodison Park.
Adama Diomande claimed a double as Hull came from behind to beat Exeter 3-1 and Swansea - winners of this competition in 2013 - beat Peterborough by the same scoreline.
Crystal Palace were 2-0 winners over Blackpool on a night when £27m signing Christian Benteke played 45 minutes on his debut, Scott Dann and Connor Wickham with goals either side of the break.
Of the non-Premier League clubs who progressed, Norwich did so in the most style with a 6-1 success over Coventry while Brighton's 4-2 victory came on the road at Oxford thanks to three late goals.
Leeds saw off Luton 1-0 thanks to a fine long-range effort from Tyler Denton on his debut, Nottingham Forest struck late to edge Millwall 2-1 and Sandro's double saw QPR see off Rochdale by the same scoreline.
Wolves saw off Cambridge 2-1 and Newcastle - who have now won three in a row in all competitions - avoided a banana skin against Cheltenham with an Ayoze Perez-inspired 2-0 triumph, the same scoreline which Preston recorded against Oldham.
More to follow...
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