Everton inflicted a potentially fatal blow to Liverpool's Premier League title hopes and took a huge step towards safety with a deserved 2-0 win over their Merseyside rivals at Goodison Park.
Liverpool, needing a win in Jurgen Klopp's final derby as manager to move level on points with leaders Arsenal, were second-best throughout as the excellent hosts claimed their first Premier League home win over the Reds since October 2010.
Jarrad Branthwaite hit the opener midway through the first half following a ferocious opening spell from Sean Dyche's side, with Dominic Calvert-Lewin capitalising on more poor Liverpool defending to head in their second from a corner after half-time.
Liverpool were unable to cope with Everton's set-piece threat and, at the other end, they were beset by familiar finishing issues as Darwin Nunez, Luis Diaz and Mohamed Salah wasted chances.
The defeat leaves Klopp's side three points behind Arsenal in second place with only four games to play and means Manchester City, who have two games in hand, can move two points above them with a win over Brighton, live on Sky Sports on Thursday.
Everton, meanwhile, now sit eight points clear of the relegation zone in 16th place, Premier League safety within their reach as they celebrate a memorable Merseyside derby triumph.
How Everton stunned sloppy Liverpool
Everton came into the game having not even scored in any of the last four Merseyside derbies but their determination to change the record was obvious from the outset.
The excellent Calvert-Lewin saw an early penalty award overturned for offside following a VAR check, but that disappointment did not affect the hosts, who continued to tear into Liverpool in transition and bombard their penalty area from set-pieces.
Ben Godfrey cleared a Salah cross-shot off the line in one of few awkward moments at the other end of the pitch, but Everton soon made a deserved breakthrough when Branthwaite stabbed a low finish over the line after Liverpool had failed to clear a free-kick.
Alisson had already bailed his side out once at that point, making a close-range save from Calvert-Lewin, who was bullying Liverpool centre-backs Virgil van Dijk and Ibrahima Konate. It was only after the goal that the visitors were able to gain any kind of foothold.
Their problem was a familiar one, though, as their finishing once again let them down. Nunez was the main culprit, shooting straight at Jordan Pickford when put through on goal, while Diaz and Andrew Robertson were also denied before the break.
Everton, emboldened by those wasted chances, came out for the second half with fresh intensity and Calvert-Lewin's towering header from Dwight McNeil's corner nearly lifted the roof off the stadium.
Liverpool tried to muster a response, going closest when Diaz cracked a diagonal effort off the post, but they could find no way past the superb Pickford despite racking up 27 shots on goal.
The result never really looked in doubt for Everton, despite those Liverpool efforts to reduce the deadlock, and Goodison Park erupted for a third time when the final whistle sounded, leaving Klopp and his players to reflect on a result which may well prove terminal to their hopes of finishing the campaign as champions.
Carra: This is the end of Liverpool's title run
Sky Sports' Jamie Carragher:
"It's Everton's night. You have to give it to them. You have to accept that as a Liverpool fan.
"This is the end of the title run for Liverpool. It almost feels like the end. They just have to make sure they finish the season strongly.
"They had enough chances in the game but at the moment they are not clinical enough in both boxes.
"I don't think you can get too angry with the team or Jurgen Klopp. It's been a great ride and a great journey. But tonight is Everton's night and you have to take it on the chin."
Klopp: I can only apologise to everyone
Liverpool manager Jurgen Klopp to Sky Sports: "I'm very disappointed. We let it become the game Everton wanted. Two goals from set pieces. They are really strong. But we created a lot and didn't score.
"Then in the second half we were emotional and in a rush, not really clear enough. Then we concede a second goal with a routine they do the whole season - we knew the ball was going there we just didn't defend it well enough.
"It was free-kick after free-kick. That was part of the story. But we weren't good enough.
"I didn't expect that performance but it happened. It's not the greatest moment we're in but you have to fight through it, use your moments to get your momentum.
"I can only apologise to everyone who is with us - it's hard for us but I know for our people it is especially hard. We should've done better but we didn't and that's why we lost."
Van Dijk: Everyone has to look in the mirror
Liverpool defender Virgil van Dijk to Sky Sports: "Very disappointed in so many ways. I think everyone has to look in the mirror, look at their own performance and if they really gave everything. Do they really want to win the league?
"We are fighting, there are games after tonight, but play like we did overall in the game like today... not winning challenges and giving the ref an opportunity to give a free-kick like he did many times, then you have no chance to win a title.
"It's a tough one and we need to do much better against a side that's (fighting) relegation. We had clear-cut chances in the first half that we should have scored but we weren't good enough and it starts with the fight. We can't let the season go out like this."
Dyche lauds 'outstanding' Calvert-Lewin
Everton boss Sean Dyche to Sky Sports: "I thought Dominic was outstanding tonight. We have been trying to get him back to where he needs to be and I think he showed it tonight.
"He gets a goal and nearly nicks one on the line. I love that about strikers, trying to get it over the line, and I think that's when he is at his best, when he is showing that energy to find that goal.
"The second was a great header but I thought, amongst many others, he was outstanding."
He added: "Jordan Pickford made some big saves in the first half. It's rare you stop these sides having chances so you need moments yourself. It's hard to pick out one or two.
"We spoke about the desire and the energy of the team and the physical side of the game. The lads did it on Sunday and they'll have to do it again. That's the challenge."
Calvert-Lewin, Pickford delight at 'special' win
Everton striker Dominic Calvert-Lewin to Sky Sports: "Pressure is a privilege and it's my responsibility to carry that.
"It's nice when you work hard and get the reward with a goal. It's extra special in a local derby. I know what it means to the fans and myself. It's a great result - we needed three points. Everything came together tonight.
"The atmosphere was extra special. Electric. It hasn't been like that for a while. To do that on a night like that is a great experience and memory. We'll kick-on now."
Everton goalkeeper Jordan Pickford to Sky Sports: "It's my first experience winning that derby at home.
"Great atmosphere, great application from the lads. A deserving and massive win. Hard work pays off.
"You have to put the hard yards in. Dom is grafting up there by himself and he gets the rewards with a goal. A clean sheet, a great team effort."
Liverpool's costly dip - Opta stats
What's next?
Everton are back at Goodison Park on Saturday when they host Brentford, live on Sky Sports. Kick-off 5.30 pm. Everton feature on Sky Sports again on Friday May 3 for their trip to relegation rivals Luton. Kick-off 8pm.
Liverpool head to West Ham on Saturday with kick-off at 12.30 pm. They return to Anfield on Sunday May 5 to host Tottenham, live on Sky Sports. Kick-off 4.30 pm.