Cody Gakpo scored his first goal for Liverpool and Mohamed Salah was on target as Everton were consigned to a 2-0 Merseyside derby defeat at Anfield.
The Reds' hopes of securing a top-four finish had been rocked by a run of four top-flight games without a win, but they got their first Premier League victory of 2023 on Monday.
Salah rounded off a blistering counter-attack 12 seconds after James Tarkowski had struck the post with his 18th goal of the season, having failed to find the back of the net in his previous five matches, late in the first half.
Gakpo got off the mark early in the second half as Liverpool moved up a spot to ninth and kept their neighbours in the relegation zone by consigning boss Sean Dyche to a first defeat, with substitute appearances for the fit-again Diogo Jota and Roberto Firmino also providing boosts for Jurgen Klopp.
Netherlands forward Gakpo spurned a good chance to open the scoring when he headed wide from close range early in a frantic start.
Tarkowski came agonisingly close to scoring a second goal in as many games after his winner against Arsenal when he rose to meet Alex Iwobi's corner with a header that struck that post, and Liverpool were in front moments later.
Everton were badly caught out on the break as Darwin Nunez darted forward and picked out Salah, who tucked into an empty net with Jordan Pickford in no man's land nine minutes before the break.
The Toffees were once again caught on the break four minutes into the second half, when Conor Cody failed to deal with Trent Alexander-Arnold's dangerous cross and Gakpo got off the mark with a tap-in.
Nunez was denied by Pickford from tight angle and bent an effort just wide after being set up by Gakpo as Everton continued to be opened up all too easily.
Ellis Simms was withdrawn after being handed a start with Dominic Calvert-Lewin unfit, before Jota and Firmino were given great ovations when they came off the bench, and Tom Davies' glaring miss with a header from close range summed up Everton's day.
Coventry City 2-3 Hull City: Tigers win five-goal thriller to keep play-off hopes alive
Hull City kept their hopes of gatecrashing the Championship play-offs alive with a thrilling 3-2 win over beaten FA Cup semi-finalists Coventry City on Wednesday.
Noah Ohio scored the winner with his first touch after coming on as a second-half substitute as Hull moved within three points of sixth-placed Norwich City with two games to play.
Coventry, meanwhile, saw their own hopes of returning to Wembley Stadium for a second successive play-off final all but ended, as they sit six points further back with three matches remaining.
Three days on from their remarkable comeback against Manchester United, the Sky Blues twice fought back to level things at Coventry Building Society Arena. Jaden Philogene's shot squirmed under goalkeeper Bradley Collins to put Hull ahead 31 minutes in, but Kasey Palmer levelled within five minutes with a stunning free-kick.
Hull went back ahead in controversial circumstances on the stroke of half-time, Liverpool loanee Fabio Carvalho converting from the penalty spot despite replays showing Joel Latibeaudiere's foul on Liam Delap took place outside the area.
Mark Robins' men again dragged themselves back into the game as Bobby Thomas headed Jay Dasilva's cross in just before the hour mark, but it was Liam Rosenior's visitors who found a winner.
Thomas went from hero to villain as his poor back pass sold Collins short, and Ohio got a toe to the ball to score the winner, keeping Hull's hopes of Premier League football intact.
Van Dijk: Liverpool have 'no chance' in title race after derby defeat
Virgil van Dijk conceded Liverpool might be out of the Premier League title race after they suffered a surprise 2-0 defeat to Everton in Wednesday's Merseyside derby.
Jarrad Branthwaite and Dominic Calvert-Lewin scored in either half to give the Toffees their first win over Liverpool at Goodison Park since 2010.
Liverpool struggled to find a way through the Toffees' defence despite dominating for long periods, and the Reds' captain says they will not outlast Arsenal and Manchester City without major improvements.
Speaking to Sky Sports, Van Dijk said: "If we play like today, then we have no chance to consider ourselves in the title race.
"We have to just focus on the next game and that will be a tough one anyway, so we will see.
"We're very disappointed, in so many ways. I think everyone has to look at their own performances. Did they really give everything, and do they really want to win the league?
"We're still fighting and there are still games after tonight, but if we play like we did overall in the game today – not winning challenges and giving the referee a chance to give free-kicks like he did many times, then you have no chance to win the title."
Dyche challenges Everton to 'go and do it again' after crucial derby victory
Sean Dyche challenged his Everton players to "go and do it again" after his team defeated Liverpool at Goodison Park in the Merseyside derby.
Everton won 2-0 on Wednesday, clinching a home victory over their local rivals for the first time since 2010 thanks to goals from Jarrad Branthwaite and Dominic Calvert-Lewin.
While it also dented Liverpool's title hopes, the victory presented a huge step forward in Everton's hopes of staying up.
They are now eight points clear of the relegation zone, with four games left to play, and the possibility of points to come back should they successfully appeal the second of their points deductions for financial breaches.
Dyche, though, insisted the job is not done as he looks towards another big game on Saturday, when Brentford visit Goodison Park.
"Very pleased with the reaction," Dyche told Sky Sports.
"This was a different game with the organisation and the belief in the organisation. They're a good side, we know that. The commitment from us had to be there. The energy of the side and also the key moments.
"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.
"We stayed focused tonight and I asked if they could stay with us and they did. Sunday was massive and now it was a massively important derby game. For people like Seamus Coleman, he wears his heart on his sleeve and he's so happy.
"We should be on 41 points and the story's different. Three clean sheets in three home games. The challenge for the players is to go and do it again."
Calvert-Lewin led the line brilliantly, converting Everton's second with a towering header early in the second half. He has scored three goals in his last four Premier League games for the Toffees, as many as in his previous 28 appearances in the competition.
"I thought [Calvert-Lewin] was outstanding tonight," Dyche said.
"We've been trying to get him back to where he needs to be and I thought he was outstanding. He gets a goal. He tried to get it over the line and I love that. The second one is a great header. No, I thought he was outstanding tonight.
"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 [players]."
SportsMax is the Caribbean sports channel of choice, committed to providing sporting content of the highest quality to the Caribbean, delivered by a team of highly innovative, passionate and qualified professionals.
(876) 619-7629
digitalmedia@sportsmax.tv
