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Ellis Simms was withdrawn after being handed a start with Dominic Calvert-Lewin unfit, before Jota and Firmino were given great ovations when they came off the bench, and Tom Davies'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.
Bayer Leverkusen 2-3 Leipzig: Visitors fightback halts unbeaten streak for Alonso's side
Bayer Leverkusen suffered their first defeat in 36 Bundesliga matches, as Leipzig came from behind to stun Xabi Alonso's side 3-2 at BayArena.
Lois Openda struck twice for Marco Rose's, who recovered from 2-0 down to make it two wins from two and move to the summit of the table.
It looked like business as usual for the reigning Bundesliga champions when they scored twice in the last seven minutes of the first half through Jeremie Frimpong and Alejandro Grimaldo.
However, Leipzig replied deep into first-half stoppage time with Kevin Kampl reducing the deficit.
Openda then brought the visitors level in the 57th minute, before a stunning long-range strike completed the turnaround 10 minutes from time, condemning Leverkusen to their first league defeat in 15 months.
Data Debrief: Leverkusen's long streak comes to a shuddering halt
Leipzig became the first side to beat Leverkusen in a Bundesliga match since Bochum achieved the feat a staggering 462 days earlier.
The visitors have begun a Bundesliga season with two wins from two for only the second time, also doing so in 2019-20.
They are also now unbeaten in 13 league matches, their longest such streak since Rose took charge.
As for Leverkusen, their invincible streak is officially history, as is their 29-game unbeaten run on home soil.
'We really let ourselves down' - Coleman slams Everton after late Bournemouth collapse
Seamus Coleman acknowledged Everton "really let ourselves down" and must "look at ourselves in the mirror" following their spectacular late collapse against Bournemouth.
Sean Dyche's side, who were seeking their first points of the season, led 2-0 in the 87th minute at Goodison Park through goals from Michael Keane and Dominic Calvert-Lewin.
However, the hosts were undone by three crosses in the latter stages, with Antoine Semenyo pulling a goal back and Lewis Cook levelling, before Luis Sinisterra completed a sensational turnaround in the sixth minute of stoppage time.
Boos rung around Goodison Park as the Toffees remained pointless and rooted to the foot of the Premier League table, and Coleman echoed the supporters' frustrations.
"We really let ourselves down in front of our fans," the skipper said. "We cannot take our foot off the gas at this level. Unfortunately, we did that.
"We cannot be conceding the goals that we did. We have to look at ourselves in the mirror."
Meanwhile, Dyche bemoaned the lack of responsibility amongst his players, as they became the first side in Premier League history to lose a game after leading by two or more goals in the 87th minute.
"We did so much right until they scored their first goal," the Everton head coach said. "The game should have been out of sight. We conceded one and then threw it away. I can't put my finger on it right now.
"They kept raining it forward and got their reward in the end. They were playing it forward and crossing it into the box, and we didn't deal with it. Simple stuff, but we threw it away. It is the third game we have thrown away this season.
"Everyone was looking at someone else to deal with things and that is when there is trouble. You could see the body language change. You have to see games through, and we have enough experience to do that, but today we didn't."
Bournemouth boss Andoni Iraola added: "It was the worst game we played this season. Everton deserved to win today, but the players kept pushing.
"I always have hope because this team has spirit. We have done it before and had some good comebacks. The spark of the first goal made us believe we could do it again."
Nottingham Forest 1-1 Wolves: Bellegarde beauty earns visitors first point
Wolves earned their first point of the Premier League season following a 1-1 draw with Nottingham Forest.
Chris Wood's towering header was cancelled out by Jean-Ricner Bellegarde's stunning strike as the spoils were shared at the City Ground.
The hosts took the lead in the 10th minute as Wood rose to nod home from Elliot Anderson's corner.
However, the visitors were level just two minutes later in spectacular fashion, with Bellegarde firing a stunning long-range volley into the roof of the net.
Gary O'Neil's side had Sam Johnstone to thank after the break, with the debutant producing a strong hand to deny Wood his second goal of the game.
Matheus Cunha curled a shot just wide while the offside flag denied Wood later on, with Forest unable to snatch victory but extending their unbeaten start to the campaign.
Data Debrief: Wolves end losing streak while Wood matches Collymore
After opening the season with two defeats and eight goals conceded, Wolves stopped the rot with a welcome point against their Midlands rivals, while ending a five-game Premier League losing streak in the process.
Meanwhile, Forest remain unbeaten in their opening three games of a top-flight season for the first time since 1995-96.
Heading his side into the lead, Wood became only the second Forest player to score in both their first two home matches in a Premier League season since Stan Collymore 30 years previously.
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
