Jota gave Liverpool a 31st-minute lead, turning home a rebound after Matt Turner had made a save.
In celebration, he ran to manager Jurgen Klopp, who handed him a miniature Diaz number seven shirt to hold aloft.
Nunez doubled Liverpool’s lead four minutes later with an emphatic near-post finish after Dominik Szoboszlai’s cut-back.
Mohamed Salah struck Liverpool’s third goal in the 77th minute, profiting from Turner’s error to slide the ball into an empty net.
Diaz was left out of the matchday squad at Anfield.
Colombia President Gustavo Petro said on Saturday that the winger’s mother had been rescued from kidnappers but the search remained ongoing for his father.
Klopp said before the match that it was a “worrying situation for all of us”.
“We had to obviously make a late change because of the private situation involving Luis Diaz,” he added.
“It was a pretty tough night. I have never had that before. It’s a new experience I never needed.”
AFP