Gerard Houllier’s Liverpool left Pride Park empty handed after falling to defeat by Derby County.
Deon Burton gave Derby an early lead before Robbie Fowler’s penalty drew Liverpool level.
Paulo Wanchope then scored either side of the interval to give Derby a two-goal cushion.
There was still time for Fowler to get his second, even if it was not enough for Liverpool to come away with a point.
The win put Derby sixth on 44 points, seven points behind fourth-placed Leeds United, while Liverpool were ninth with 39 points.
Steven Gerrard’s hat-trick earned Liverpool their biggest victory in a Merseyside derby in nine years.
It also extended Everton manager David Moyes's wait for a win at Anfield to 10 years.
Gerrard scored in the first half and then twice after the break to end Liverpool's winless run of four PL matches.
The result ended Everton's 10-match unbeaten run in all competitions.
It put five points between the two sides as well. Liverpool were seventh on 42 points, while Everton sat ninth.