Premier League 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 on Tuesday.
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 though 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.
But top-flight new boys Crystal Palace lost 2-1 at Bristol City of third tier League One.
Second-half goals from Jay Emmanuel-Thomas and Scott Wagstaff sealed victory for the host, with Owen Garvan grabbing a consolation goal for a Palace side where manager Ian Holloway had made 11 changes from the team beaten 2-1 by Stoke in the Premier League on Saturday.
Palace's top-flight rivals Sunderland had to come from two goals down before beating League One Milton Keynes Dons 4-2 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 put the result beyond doubt 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 the Premier League through after they fought back from behind in extra-time against their fourth division 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 forced spot-kicks when he levelled with three minutes to spare.
Elsewhere Sweden international Johan Elmander marked his full Norwich debut with two goals in the Premier League side's 6-3 win over Bury.
Meanwhile it wasn't until the 10th minute that Robbie Brady scored the goal that saw Hull edge out Leyton Orient at the League One leaders' Brisbane Road ground in east London.