Liverpool squandered a two-goal lead before seeing off third-tier Notts County 4-2 in extra-time in the second round of the League Cup at Anfield.
Raheem Sterling celebrated his senior England call-up by opening the scoring for Liverpool in the fourth minute before Daniel Sturridge scored his third goal in as many games to make it 2-0 before half-time.
However, County responded through a Yoann Arquin header before substitute Adam Coombes struck an equaliser with six minutes of normal time remaining.
Liverpool kept their cool in extra-time and secured a 4-2 win with a second goal from Sturridge and a fourth in all from Jordan Henderson.
Elsewhere, top-flight new boys Crystal Palace lost 2-1 at Bristol City of the third-tier League One.
Second-half goals from Jay Emmanuel-Thomas and Scott Wagstaff sealed victory for the hosts, with Owen Garvan grabbing a consolation goal for a Palace side featuring 11 changes from Saturday's defeat at Stoke.
Sunderland had to come from two goals down before beating Milton Keynes Dons of League One at the Stadium of Light.
Goals from Patrick Bamford and Izale McLeod gave Milton Keynes hope of a shock win before Jozy Altidore scored for Sunderland with just 12 minutes left.
Connor Wickham equalised three minutes from time before scoring Sunderland's third goal in the 89th minute.
Adam Johnson secured a 4-2 victory deep into injury time.
There were no such worries for Southampton as they thrashed bottom of the second-tier Championship Barnsley 5-1.
However, Fulham needed penalties to see off League Two Burton after a 2-2 draw at the Pirelli Stadium.
Fulham goalkeeper David Stockdale saved the vital spot-kick from Phil Edwards to send his side through after they fought back from behind in extra-time against their League Two opponents.
Adel Taarabt scored his first goal for Fulham in the 36th minute, but Jack Dyer forced extra-time with an 85th-minute equaliser. Michael Symes put the League Two side ahead in the first period of extra-time, but Hugo Rodallega levelled with three minutes to spare.
Sweden international Johan Elmander marked his full Norwich debut with two goals in his side's 6-3 win over Bury, while a Robbie Brady goal saw Hull edge out Leyton Orient.