Liverpool remained seventh in the table but moved five points ahead of their local rivals whose manager David Moyes endured a miserable evening to mark 10 years in charge of the Goodison Park club.
Gerrard had the first clear chance to open the scoring when his late run took him clear of the Everton defence after seven minutes but his low shot was well saved by the sprawling Tim Howard.
The home side dominated the early stages with some crisp attacking football, Luis Suarez causing problems with his darting runs and clever movement, and they made the breakthrough after 34 minutes.
Howard blocked a shot from Martin Kelly and when the ball broke to Gerrard just inside the penalty area he delicately chipped it over the stranded goalkeeper and into the net.
Suarez's persistence earned the second Liverpool goal, his mazy dribble along the goal line setting up Gerrard to smash the ball high into the net from eight metres shortly after halftime.
A toothless Everton never threatened to get back into the match and Gerrard completed his hat-trick from close range following a pass by Suarez deep into stoppage time.
