Liverpool and Everton enjoyed big wins in the English League Cup on Tuesday, while Chelsea was pushed hard by third-tier Bristol Rovers before also reaching the third round.
Daniel Sturridge came off the bench to score two goals and wrap up Liverpool's 5-0 win at Burton Albion, a second-tier side managed by former Liverpool forward Nigel Clough.
Everton also had a substitute striker scoring a late double, with Arouna Kone's goals sealing a 4-0 home win over Yeovil.
Chelsea's decision to field a team largely made up of reserve players nearly backfired in a 3-2 win at Stamford Bridge. BatshuayiMichy Batshuayi scored twice for Chelsea.
Stoke, Swansea, Hull and Crystal Palace were other Premier League teams to progress to the third round, when clubs involved in Europe enter the competition.