Liverpool responded to Manchester City's thrashing of Norwich by recording a hard-fought 1-0 win at Burnley.
Fabinho struck the only goal in the first half, as the Reds continued their fine set-piece record on a day when set-plays proved decisive across the Premier League.
Elsewhere, Raul Jimenez starred as Wolves leapfrogged Tottenham with a shock 2-0 win, and Newcastle continued their revival with a 1-0 win over Aston Villa, thanks to Kieran Tripper's free-kick.
The final game of the day saw West Ham rescue a dramatic 2-2 draw at Leicester City, with Craig Dawson netting a stoppage-time equaliser.
Burnley 0-1 Liverpool: Reds reap rewards of set-piece focus
Liverpool did not produce a vintage performance, but Jurgen Klopp's men kept leaders Manchester City on their toes by earning a vital away win.
The Reds had to work hard for the three points against Burnley at Turf Moor. After managing 27 shots, nine attempts on target and 50 touches in Burnley's penalty area in the reverse fixture at Anfield last August, Liverpool had just over half as many touches in Burnley's 18-yard box this time (26), managing 12 shots in total and just four on target.
However, Klopp's men dug deep to find a winning goal, and did so courtesy of their fantastic set-piece record. Excluding penalties, 14 of Liverpool’s 61 Premier League goals this season have come via set-pieces, more than any other team and more than the tally they recorded in the top-flight last term (13).
Fabinho's winning goal also means he has scored more goals in his last seven matches (five) than he managed in his first 142 appearances for Liverpool in all competitions (four).
Meanwhile, the Anfield outfit also maintained their record of having won each of their games in which the Brazilian has netted for the club, with that run now reaching eight matches.
Tottenham 0-2 Wolves: Jimenez proves decisive at Spurs once again
It was Wolves, rather than Tottenham, who asserted their top-four credentials by recording a huge win in north London, with Jimenez and Leander Dendoncker firing the visitors to a 2-0 win.
Mexican striker Jimenez has now scored in each of his last three Premier League appearances away at Spurs (three goals), with Wolves winning each of those contests.
Indeed, Jimenez has now scored four times in six appearances against Tottenham, and has only scored more Premier League goals against Southampton and Everton (five).
For Antonio Conte's Spurs, the defeat was their third Premier League reverse in succession, and they also lost three consecutive league games under Nuno Espirito Santo in September 2021. This marks the first time they have had multiple three-match losing games in a Premier League campaign since 2004-05 (also two).
Newcastle 1-0 Aston Villa: Another free-kick continues Toon revival
Newcastle's clash with Aston Villa was not exactly one for the purists, featuring the third-lowest expected goals tally of the entire Premier League season so far, but Tripper ensured that it was a memorable day for the Magpies.
Trippier's 35th-minute free-kick was enough to see off Steven Gerrard's men in a contest where both teams created just 0.5 xG apiece.
Remarkably, Newcastle have now scored a direct free-kick goal in each of their last three Premier League games (Jonjo Shelvey at Leeds, followed by Trippier against Everton and Aston Villa), becoming the first side to do so since Liverpool in December 2013.
In a game of fine margins, the England right-back showed the quality that he brings to the Magpies' relegation fight, and he is now the first Newcastle player to score direct free-kick goals in consecutive Premier League games since Hugo Viana did so in May 2003.
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."
Howe: Newcastle performance in Palace defeat 'way off' Spurs win
Eddie Howe admitted Newcastle United's performance in the 2-0 loss at Crystal Palace on Wednesday was "way off" the one that saw them thump Tottenham in their previous game.
Howe's men hammered Spurs 4-0 in their last match, but they never got close to matching the attacking verve from that outing and a Jean-Philippe Mateta double condemned the Magpies to defeat at Selhurst Park.
Newcastle didn't even manage a shot on target until the 87th minute, accumulating just 0.42 xG (expected goals) as the likes of Alexander Isak and Anthony Gordon struggled to make an impact.
Only against Manchester City in August (one) have Newcastle recorded fewer shots on target in a Premier League game this season than their two against Palace, and Howe was critical of his team's display in the loss, one that all but ends their hopes of finishing in the top four.
"[It is a] bad day for us," Howe told Newcastle's club media.
"I thought we were disappointing today, especially in the first 60 minutes. We were way off our levels against Tottenham and our best levels.
"I thought technically we didn't deliver a good performance, and out of possession I don't think it was a particularly good performance either."
Newcastle were unlocked twice for Mateta to score by a Palace side who themselves only generated 0.88 xG.
Howe was left frustrated by the manner in which his side conceded, adding: "I think we'll be disappointed with our performance technically today, and that's probably epitomised by the two goals where we're disappointed with how we've given them the ball in those situations and then how we defended.
"I think the goals sum up aspects of our performance where there was some good, lots of moments that could have led to opportunities, but we were slow to shoot around the box," he said.
The defeat, combined with Manchester United's 4-2 win over Sheffield United, means Newcastle drop to seventh, while eighth-placed West Ham are two points behind with a game in hand.
Newcastle have now lost eight of their last 11 Premier League away games, while they have lost on four occasions in London in the league this term, only doing so more times in a Premier League season in 2000-01 and 2005-06 (both five).
It's been a disappointing season for Howe and his side, especially compared to the heroics of last term when Newcastle finished in the top four, and the Magpies boss knows there's work to be done to get back to those levels.
"It's a day that we have to take our punishment, deal with it, and then try and improve," Howe continued. "It's frustrating because we know we're capable of much better."
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]."
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