Jurgen Klopp labelled Divock Origi as a "legend on and off the pitch" after his introduction steered the Merseyside derby Liverpool's way.
With the game poised at 0-0 with an hour played, Origi was brought on alongside Luis Diaz as Klopp substituted Naby Keita and Sadio Mane.
Within two minutes Origi had cushioned a pass into Mohamed Salah's path and his cross was headed home by Andy Robertson to break the deadlock.
Origi then made the result secure late on with a close-range header as Liverpool closed the gap on Premier League leaders Manchester City to just a point.
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It was the Belgium international's sixth career goal against Everton and Klopp was delighted with the contribution of a player who could yet walk away from Anfield this summer as a free agent amid reported interest from Italy.
“He is a legend on and off the pitch," Klopp said. "He is a fantastic footballer for me, and I know it sounds ridiculous as I don’t line him up often, he is a world-class striker, he is our best finisher, definitely.
"He always was and everybody would say the same when you see him do these kinds of things in training, then you see the quality of the squad and other players and it’s really hard I imagine (for him).
"Other players were not in the squad but in really good shape, I have really hard decisions to make because the boys all want to contribute and are responsible for the situation we are in.
"Everybody loves Div and rightly so. He was again very decisive. I’m very, very happy for him."