Chelsea came from behind at Aston Villa to move five points clear in fourth as two goals in as many second-half minutes earned them a 2-1 win.
Raheem Sterling, Kevin De Bruyne and Phil Foden were on target as Manchester City impressed on their Premier League restart with a convincing 3-0 win over 10-man Arsenal at a wet Etihad Stadium.
The Premier League faces a week of chaos after hopes of government direction on Project Restart were dashed by the prime minister.
Frank Lampard came out on top against his former Chelsea boss Carlo Ancelotti by masterminding a 4-0 victory over Everton on Sunday.
The Premier League has been told by the government it must show some matches free-to-air and put more money into the Football League and grassroots game as a condition for restarting this season.
The English top-flight has followed the lead of Serie A, La Liga, MLS and Ligue 1 by announcing that all upcoming fixtures will have to be rearranged
Liverpool won a record 22nd straight home game in the league thanks to goals from Mohamed Salah and Sadio Mane against Bournemouth.
The UK government has given permission for the Premier League and other professional sports to return behind closed doors from 1 June, providing its five tests on controlling the coronavirus are met.
Manchester United completed a league double over Manchester City to leave Liverpool on the verge of a first Premier League title.
Goals from Willian and Ross Barkley, plus some excellent saves from Kepa Arrizabalaga, helped Chelsea reach the quarter-finals.
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