Willian and Ross Barkley were on target as Chelsea consigned Liverpool to a third defeat in their past four matches.
Chelsea dumped Liverpool out of the FA Cup with a 2-0 victory at Stamford Bridge, while Newcastle United and Sheffield United also moved into the quarter-finals on Tuesday.
Watford inflicted a shock first Premier League defeat on runaway leaders Liverpool on Saturday and they suffered a third loss in their past four games in all competitions three days later.
Adrian’s howler gifted Willian the opening goal 13 minutes in and there was no way back for Jurgen Klopp’s side after Ross Barkley doubled Chelsea’s lead in the second half.
Kepa Arrizabalaga impressed on his return to the Chelsea team, making a flurry of saves in quick succession in the first half on a frustrating evening for a much stronger Reds side than they fielded in previous rounds.
Newcastle reached the last eight for the first time since 2006, ending their goal drought to beat Championship leaders West Brom 3-2.
The Magpies had gone three games without a goal, but Miguel Almiron’s first-half brace and Valentino Lazaro’s finish put them three up.
Matt Phillips pulled one back and although Kenneth Zohore added a second in stoppage time, that could not prevent Newcastle from putting their name in the hat.
Sheffield United needed extra time to get past Reading, Billy Sharp nodding in the winner after a George Puscas penalty cancelled out David McGoldrick’s opener.