Watford and West Brom were the big casualties in the second round of the EFL Cup while the rest of the Premier League sides in action on Tuesday night all advanced in normal time.
Watford went down 2-1 at Gillingham after extra time.
The Hornets were eight minutes from progressing themselves having led through Odion Ighalo but Mark Byrne levelled and Bradley Dack, who had missed a penalty in the second half, grabbed the winner in the 102nd minute to eliminate last year's FA Cup semi-finalists.
Tony Pulis' West Brom also squandered a lead they had held up until the 82nd minute as Northampton booked their passage through to the third round courtesy of a 4-3 penalty shoot-out success.
The Cobblers led through Zander Diamond and though West Brom went ahead after strikes from James McClean and Gareth McAuley, Alex Revell forced extra-time as he made it 2-2.
The extra half hour finished without further goals to send the match to a shoot-out. Saido Berahino missed from 12 yards and James Morrison's effort was saved, allowing Kenji Gorre to convert and eliminate the Baggies.
The seven other top-flight sides encountered few problems. Antonio Conte's Chelsea were made to sweat by League One Bristol 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.
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.
Shane Duffy marked his return to the Blackburn side with the winner in their topsy-turvy tie with Crewe, who were beaten 4-3 after extra time in front of just over 3,000 at Ewood Park.
Duffy, who had been suspended following his dismissal at Cardiff, when he scored two own goals, headed home after Rovers had fought back from being 2-0 down early on.
Derby needed a marathon penalty shoot-out to knock out Carlisle, the Rams eventually going through 14-13 following a 1-1 draw after 120 minutes.
Reading also went through on spot-kicks having drawn 2-2 with MK Dons, though the manner of their victory on penalties was considerably smaller at 4--2.
Championship clubs Leeds, Nottingham Forest, QPR, Wolves and Bristol City were all victors by one-goal margins over Luton, Millwall, Rochdale, Cambridge and Scunthorpe respectively.