The result leaves the Blues five points clear of their city rivals in the race for a European place and keeps David Moyes and his team on course for a second successive league finish above the Reds.
Everton's central defensive partnership of Phil Jagielka and Sylvain Distin comfortably dealt with Liverpool's attacking threat, but Moyes and his team were also short of a danger up front at Anfield.
The points might have been shared in the two derby matches this season, but refereeing decisions evened up after the events at Anfield on Sunday.
Everton defender Distin appeared to have broken the deadlock early in the second half at Anfield, but match official Michael Oliver adjudged Blues striker Victor Anichebe to have impeded Liverpool goalkeeper Pepe Reina when Leighton Baines' corner arrived in the area.
Moments before the disallowed goal, Anichebe had been spoken to by Oliver for tussling inside the area, but the forward was not at fault at Baines' set piece, and Reina appeared to have lost his footing.
There is an old cliché in football that refereeing decisions even themselves up over a season, though. And Liverpool supporters can be forgiven for highlighting another refereeing decision that denied them victory in the first Merseyside derby of the season at Goodison Park.
Everton had hauled themselves back from two goals down to 2-2 and were defending a corner which Suarez turned home.
Liverpool captain Gerrard was so convinced that the goal was legitimate that he went on an 80-yard celebration slide to finish in front of the visiting supporters at Goodison.
But referee Andre Marriner adjudged the Uruguay international was offside when he scored, and the late "winner" was not allowed.