Jarrad Branthwaite scored his third goal of the season for Everton
Jarrad Branthwaite's first-half goal and a towering header from Dominic Calvert-Lewin after the break gave Everton their first Merseyside derby win at home since October 2010 in a victory that could assume huge significance.
Liverpool knew a win over the rivals they have dominated so often would put them level on points with leaders Arsenal but Jurgen Klopp's side never recovered from an opening period when they were overpowered by Everton, Branthwaite's close-range finish a deserved reward.
Everton then needed England keeper Jordan Pickford to keep them ahead as he saved from Darwin Nunez, Luis Diaz and Andy Robertson - but on this night, in a fiercely hostile atmosphere, the Toffees were not to be denied.
And victory was effectively sealed when Calvert-Lewin, a constant threat, rose at the far post to head home from Dwight McNeil's corner at the far post, just before the hour.
Liverpool had plenty of possession but, with Everton's defence resolute and Pickford so impressive, there was no way back as Klopp tasted defeat at Goodison Park in his final Merseyside derby.
-- Courtesy of BBC Sport