Gerrard was returning to the side after two games out through injury and opened the scoring with a superb lofted finish after good link-up play put Martin Kelly in on goal.
The Reds’ captain doubled the lead with a powerful close-range drive shortly after the break after great work by Luis Suarez down the right.
And Suarez laid on the third in stoppage time to cap the hat-trick.
Liverpool dominated the game from star to finish and probably should have won by more. Andy Carroll and Suarez linked up brilliantly, with Carroll putting in one of his best performances for the club.
Kelly was also superb and was – again – close to scoring from a superb Stewart Downing cross at the Kop end.
Next up for Kenny Dalglish’s side is the FA Cup quarter final with Stoke on Sunday.
Gerrard on his hat-trick:
“To get three goals is a bit extra but I have to give Luis Suarez a special mention. He put two on a plate for me. I haven’t played with him much but when I have we have an understanding. Hopefully that can continue.
“It’s been a frustrating run for us, we never turned up at Sunderland and we are going from one extreme to the other at the moment. We need a winning streak.”
Liverpool: Reina, Kelly, Carragher, Skrtel, Enrique, Henderson (Kuyt 72), Spearing, Gerrard, Downing, Suarez, Carroll.
Subs not used: Doni, Coates, Flanagan, Shelvey, Adam, Maxi
Goals: Gerrard (34, 51, 90)
Everton: Howard, Hibbert, Distin, Jagielka, Baines, Coleman (Drenthe 61), Fellaini, Pienaar, Rodwell, Stracqualursi (Osman 61), Anichebe (Jelavic 61).
Subs: Mucha, Heitinga, Cahill, Neville.
Referee: Phil Dowd