However, League One teams Oxford, Burton and Sunderland all knocked out Premier League teams.
Oxford accounted for West Ham, who made made nine changes and paid for it it as they were embarrassed 4-0, with goals from Elliott Moore, Matty Taylor, Tarique Fosu-Henry and Shandon Baptiste in the second half.
Max Power’s ninth-minute long-range strike gave Sunderland a 1-0 victory over top-flight opponents Sheffield United, who made 10 changes.
Last season’s beaten semi-finalists Burton continued their love affair with the competition by winning 2-0 at home to the Premier League’s fifth-placed team Bournemouth, who also made 10 changes.
Oliver Sarkic put them ahead in the 14th-minute and Nathan Broadhead’s late goal secured victory over a team 52 places above them.
Liverpool, who fielded a completely different XI, including debuts to Harvey Elliott, goalkeeper Caoimhin Kelleher and Rhian Brewster, were 2-0 winners at League One MK Dons.
Elliott, at 16 years and 174 days the youngest player to start a competitive match for the club, hit the crossbar in both halves but it was the experienced James Milner who was the key man.
In the first half, goalkeeper Stuart Moore spilled his driven shot and could only palm the ball into the net at the second attempt and after the break Milner provided the assist for defender Ki-Jana Hoever to score his first for the club in only his second appearance.
Chelsea secured their first home win under Frank Lampard with a 7-1 victory against League Two Grimsby with goals from Ross Barkley, Michy Batshuayi (2), Pedro, Kurt Zouma, Reece James and Callum Hudson-Odoi.
Aston Villa won the all-Premier League tie at Brighton, giving debuts to seven academy players as they won 3-1 thanks to goals from Jota, Conor Hourihane and Jack Grealish.
Reading’s Lucas Boye scored an equaliser in the ninth minute of added time to cancel out Cavaco Jordao’s opener but missed a penalty in the shootout as Wolves prevailed 4-2 on spot-kicks.
Chelsea’s reward in the fourth round is a home tie against Manchester United while Arsenal will travel to Liverpool.
The two lowest-ranked sides left in the competition, League Two pair Crawley and Colchester, drew each other.
FOURTH ROUND DRAW:
- Everton v Watford
- Aston Villa v Wolves
- Manchester City v Southampton
- Burton v Leicester
- Crawley v Colchester
- Chelsea v Manchester United
- Oxford v Sunderland
- Liverpool v Arsenal
- (Ties to be played week beginning October 28).