Everton have beaten Liverpool in the Premier League for their first win at Anfield in 22 years while Chelsea dropped points in the battle for a top-four spot.
A first win at Anfield since 1999 for Everton. The worst form for Liverpool at home in the league since 1923 after a fourth straight loss.
The English title that took 30 years to win again is being surrendered far too easily by Liverpool.
Richarlison scored after three minutes and substitute Gylfi Sigurdsson netted a late penalty to give Everton a 2-0 Premier League victory.
"We did well from a creating point of view - but we had to chase the game, and if we have to do that, I think you saw the finishing situation," Liverpool boss Jurgen Klopp told Sky Sports.
"We were not calm enough in these moments when we should have been calmer, that's the truth, when we could have been calmer."
A first Merseyside derby win since 2010 put Everton behind sixth-place Liverpool only on goal difference while the champions are 16 points adrift of leaders Manchester City.
"I'm really pleased and really happy for the club, for the supporters," Everton boss Carlo Ancelotti said.
"I hope for sure they are going to celebrate tonight. It was a good performance, a lot of effort, a lot of spirit."
The only disappointment for Ancelotti's side will have been not having any fans allowed into the home of their greatest rivals, due to the pandemic, to see the landmark triumph.
Chelsea are in the fourth and final Champions League place after drawing 1-1 at Southampton.
Even worse for Liverpool was losing yet another centre back option as Jordan Henderson was forced off injured in the first half.
"Groin, adductor region, so that's not good, but we don't know exactly. The rest we will know tomorrow," Klopp said.
October's derby was the start of Liverpool's problems when Virgil van Dijk was ruled out for the season with an ACL injury after a reckless tackle by Everton goalkeeper Jordan Pickford.
They have had 18 different central defensive pairings since, ending Saturday's game with the inexperienced duo of Ozan Kabak and substitute Nat Phillips.
Meanwhile, Chelsea manager Thomas Tuchel criticised Callum Hudson-Odoi after hauling him off in the draw at Southampton - only 31 minutes after the England international replaced the injured Tammy Abraham at halftime.
"I was not happy with his attitude, energy and counter-pressing... I had the feeling he was never really into the game," Tuchel said of Hudson-Odoi.
Takumi Minamino's fine finish put the Saints ahead in the 33rd minute before Mason Mount equalized in the 54th from a penalty after he was brought down in the box by Danny Ings.
West Brom overcame Semi Ajayi's first-half red card for denying a goalscoring chance to draw 0-0 draw at 15th-place Burnley, leaving Sam Allardyce's visitors 11 points from safety.
Fulham's first home league victory since November took them within three points of safety as they defeated rock-bottom Sheffield United 1-0 courtesy of Ademola Lookman 61st-minute goal.