Liverpool, Everton, Chelsea, Stoke and Swansea are among the Premier League sides advancing in the League Cup.
Watford and West Bromwich Albion were beaten by third-tier opposition in the English League Cup on Tuesday, while fellow Premier League sides Liverpool and Everton enjoyed big wins in the second round.
Chelsea was pushed hard by third-tier Bristol Rovers before also advancing to the third round with a 3-2 win at Stamford Bridge.
Watford lost 2-1 to Gillingham after extra time and West Brom was beaten 4-3 on penalties by Northampton after they finished 2-2 after 120 minutes.
Northampton famously ousted Liverpool in the 2010-11 competition, but the Reds easily avoided a so-called "giant-killing" this time round by thrashing Burton Albion 5-0. Daniel Sturridge came off the bench to score two goals and wrap up victory over the second-tier side managed by former Liverpool forward Nigel Clough.
Divock Origi and Roberto Firmino also scored for a full-strength Liverpool team, and there was an own goal.
"Very serious, very professional performance by my side," said Liverpool manager Jurgen Klopp, who added that second-half injuries to Emre Can and Origi were not serious.
Everton also had a substitute striker scoring a late double, with Arouna Kone's goals sealing a 4-0 home win over fourth-tier Yeovil.
Chelsea manager Antonio Conte's decision to field a team largely made up of reserve players nearly backfired. Belgium striker Michy Batshuayi scored two first-half goals as Chelsea took a 3-1 lead into halftime, before Rovers scored a 48th-minute penalty and struck the crossbar as they went in search of an equalizer.
Devoid of European football this season, Liverpool and Chelsea will likely take the League Cup seriously. They are two of the most successful clubs in the competition's history, having won it 13 times between them.
Stoke, Swansea, Hull and Crystal Palace were the other Premier League teams to progress to the third round, when clubs involved in Europe enter the draw that takes place Wednesday.
Peter Crouch scored a hat trick—including one goal from a scissor kick—in Stoke's 4-0 win at Stevenage, Oliver McBurnie scored twice on his debut for Swansea in a 3-1 win at Peterborough, Hull beat Exeter 3-1 away and Palace was a 2-0 winner at home to Blackpool.
Palace gave a debut to new record-signing Christian Benteke, who played the first half before being substituted.
Derby beat Carlisle 14-13 on penalties to equal the most goals scored in a shootout in the competition's history.