The 217th meeting between the clubs ended as a one-sided affair with the Reds scoring once in the first half and twice in the second to make it seven wins from the past 11 derbies.
Gerrard marked his 400th Premier League appearance in style by taking the Man of the Match honours along with his treble of goals on a night to remember for Kenny Dalglish and his men.
Both sides were busy in attack early but the opening goal came to the home side in the 34th minute when captain Gerrard produced a brilliant finish with his left foot. The ball had fallen to Martin Kelly on the right side of the area but his attempt was kept out by a sliding Tim Howard with the deflection bouncing off Sylvain Distin and into the path of Gerrard who dinked a beautiful shot over the waiting Toffees defence from the edge of the area, igniting the Anfield crowd.
Six minutes into the second half, Liverpool were two ahead when Luis Suarez made a determined run into the area and down the byline before leaving it for a marauding Gerrard to hammer home emphatically from six yards.
In injury-time, Liverpool's night was made even better when Gerrard completed his hat-trick with a second left-footer of the encounter after being teed up by Suarez who had earlier exchanged passes with the midfield general.
It was his second Premier League treble and made him the first man in 76 years to score three in a Merseyside derby at Anfield and the first since Ian Rush to complete a hat-trick for the Reds against the Toffees.
The victory ended a three-game losing streak for Liverpool, who are now two points behind sixth-placed Newcastle United, whilst the loss was the first in eight for David Moyes' ninth-placed side with the Scotsman's 10-year celebrations tomorrow to be somewhat dampened.
Anfield, Liverpool - 44,921