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Manchester City and Arsenal suffered shock defeats in the tenth round.
Diaz scored more Premier League goals against United than any other opponent.
Every team will play eight games against different opponents in the new format of Europe's elite club competition.
Diogo Jota opened the scoring in a 2-0 win against newly-promoted Ipswich Town.
The Dutchman was in charge of Eredivisie side Feyenoord.
Strikes from Mohamed Salah, Andy Robertson, Cody Gakpo and Harvey Elliott earned the victory for Klopp's men, who had won one of their previous five league games and seen their title challenge crumble.
Salah seemed to have a different perspective and refused interviews with reporters in the mixed zone, saying: 'There's going to be fire today if I speak.'
Liverpool remain third on 75 points, one behind second-placed Manchester City, who have played two games fewer, and two behind first-placed Arsenal, who have a game in hand and a much-superior goal difference.
Everton's first derby victory at Goodison Park in more than 13 years prevented Liverpool from climbing level with Arsenal at the top of the league table. Juergen Klopp's men are three points behind the Gunners (77) with four games to play.
Arsenal lead on 74 points, one point ahead of Manchester City.
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