League One trio Peterborough United, Swindon Town and Tranmere Rovers all knocked out Championship opposition, while Birmingham City won a controversial game against Yeovil Town on penalties.
Norwich City and Southampton were in rampant mood en route to the third round, while West Bromwich Albion and West Ham United also safely progressed.
Second-half goals from Jay Emmanuel-Thomas and Scott Wagstaff helped Bristol City to a 2-1 win over a much-changed Crystal Palace at Ashton Gate.
Sunderland appeared to be on the brink of a shock defeat when trailing MK Dons 2-0 with 12 minutes to go, but a Connor Wickham brace helped to secure a 4-2 success.
Notts County recovered from two goals down to force extra-time at Anfield before goals from Daniel Sturridge and Jordan Henderson provided Liverpool with a 4-2 win.
Lee Tomlin plundered a hat-trick, including a brace of second-half penalties, as Peterborough thumped Reading 6-0 at London Road.
Goals from Nile Ranger and Alex Pritchard saw Swindon cause an upset after the League One side won 2-0 against QPR at Loftus Road.
Hull City needed extra-time to squeeze into the third round as Robbie Brady's goal in the 107th minute saw off in-form Leyton Orient at Brisbane Road.
Hugo Rodallega scored a 117th minute equaliser before John Arne Riise struck the winning penalty in the shoot-out as Fulham overcame Burton following a 2-2 draw at the Pirelli Stadium.
Tranmere knocked out Bolton Wanderers 4-2 in a penalty shoot-out following a 1-1 draw at Prenton Park.
Goals either side of half-time from Ricardo Vaz Te and Ravel Morrison helped West Ham United to a 2-1 home win over Cheltenham Town.
Steven Davis scored a goal in each half as Southampton eased to a 5-1 victory over Barnsley at Oakwell.
Saido Berahino marked his first start for West Bromwich Albion with a first-half hat-trick in a comfortable 3-0 home win over Newport County.
Birmingham beat fellow Championship side Yeovil 3-2 on penalties after a 3-3 draw at Huish Park which was shrouded in controversy following a late equaliser from the hosts in normal time.
Swedish duo Martin Olsson and Johan Elmander celebrated their first starts for Norwich City by getting on the scoresheet in a 6-3 triumph over Bury at Carrow Road.
Leeds United got the better of Doncaster Rovers in a Yorkshire derby as goals from Matt Smith and Ross McCormack in the space of three second-half minutes earned a 3-1 win at the Keepmoat Stadium.
In another all-Championship affair, Huddersfield Town twice came from behind to beat Charlton Athletic 3-2 thanks to Adam Hammill's 82nd minute winner.
Kieran Trippier and Danny Ings scored first-half goals as Burnley saw off local rivals Preston North End 2-0 at Turf Moor.
Chris Wood scored a hat-trick as Leicester City recovered from conceding an early goal to run out 5-2 winners away to League One side Carlisle United.
Chris Martin and Conor Sammon both scored a brace as Derby County had little trouble in thrashing Brentford 5-0 at Pride Park.