Divock Origi, Roberto Firmino and Sturridge all scored as Liverpool, last season’s beaten finalists, crushed Championship side Burton, who are managed by ex-Liverpool midfielder Nigel Clough.
Michy Batshuayi marked his full Chelsea debut with a brace against Bristol Rovers, while Victor Moses was also on target as manager Antonio Conte enjoyed a third straight competitive win.
Premier League sides Crystal Palace, Everton, Hull City, Swansea City and Stoke City also went through, Peter Crouch scoring a hat-trick for Stoke in a 4-0 win at Stevenage.
But Watford and West Bromwich Albion were both taken to extra time by third-tier opposition, the former drawing 1-1 at home to Gillingham, the latter held 2-2. Mane teed up Origi to break the deadlock for Liverpool with a clever back-heel in the 15th minute before Nathaniel Clyne crossed for Firmino to head in the visitors’ second goal.
A Tom Naylor own goal just after the hour made it 3-0 and Sturridge came off the bench to complete the rout with a late brace, tapping in James Milner’s cross and slamming home from Mane’s pass.