Things were less straightforward for Chelsea against League One side Bristol Rovers as they held off a fightback to eventually win 3-2.
Arouna Kone scored twice in the final 10 minutes to help Everton to a 4-0 win over Yeovil Town at Goodison Park on a night that also saw Ashley Williams and Yannick Bolasie make their first starts for the Toffees.
Christian Benteke was another to be handed a debut as Crystal Palace overcame Blackpool 2-0, while Hull City and Swansea City both recorded 3-1 victories away from home to Exeter City and Peterborough United respectively.
There were shocks for West Bromwich Albion and Watford, though, with the Baggies losing on penalties to League One side Northampton Town, while the Hornets were beaten at home by Gillingham after extra time.
Arguably the match of the round came at Ewood Park where struggling Championship side Blackburn Rovers overcame their poor start to the season and a fan boycott to beat Crewe Alexandra after extra time, although they were forced to come from two goals down en route to sealing a dramatic 4-3 victory.
Craig Conway appeared to have wrapped up the win in normal time with an 88th-minute strike, but Crewe's Chris Dagnall forced an additional 30 with a 93rd-minute equaliser before Shane Duffy - scorer of three own goals already this season - found the right net this time to finally clinch the victory.
Norwich City were the highest scorers of the night with a 6-1 thrashing of Coventry City, while fellow Championship outfits Leeds United, Nottingham Forest, Newcastle United, Brighton & Hove Albion, Preston North End, Queens Park Rangers, and Wolverhampton Wanderers also avoided defeat to lower-league opposition.
There was also a shootout at the iPro Stadium between Derby County and Carlisle United after the League Two visitors scored a 95th-minute equaliser, but the Rams eventually won a thrilling shootout 14-13.
Results in full: Crystal Palace 2-0 Blackpool, Blackburn 4-3 Crewe (AET), Burton 0-5 Liverpool, Chelsea 3-2 Bristol Rovers, Derby 1-1 Carlisle (14-13 on pens), Everton 4-0 Yeovil, Exeter 1-3 Hull, Luton 0-1 Leeds, Millwall 1-2 Nottingham Forest, Newcastle 2-0 Cheltenham, Northampton 2-2 West Brom (4-3 on pens), Norwich 6-1 Coventry, Oxford 2-4 Brighton, Peterborough 1-3 Swansea, Preston 2-0 Oldham, QPR 2-1 Rochdale, Scunthorpe 1-2 Bristol City (AET), Stevenage 0-4 Stoke, Watford 1-2 Gillingham (AET), Wolves 2-1 Cambridge, Reading 3-2 MK Dons (4-2 on pens)