Divock Origi kept up his run of scoring against Everton as his late goal helped Liverpool claim a 2-0 win in the Merseyside derby.
The Reds were made to work hard by struggling Everton, who went into Sunday's match in the relegation zone after Burnley had defeated Wolves earlier on.
Liverpool are now back within a point of their Premier League title rivals Manchester City, while third-placed Chelsea moved five points clear of fourth-placed Arsenal with a last-gasp win over West Ham.
Brighton and Hove Albion and Southampton played out a 2-2 draw in the day's other game. Here, using Opta data, Stats Perform checks the best facts from Sunday's action.
Chelsea 1-0 West Ham: Pulisic spares Jorginho's blushes
Chelsea turned in a below-par performance against West Ham, but got over the line thanks to Christian Pulisic's last-gasp winner.
The Blues had lost their previous two matches at Stamford Bridge and looked set to be on their way to a third home game without a win when Jorginho sent a poor penalty straight at Lukasz Fabianski.
Jorginho had converted each of his last 13 penalties for Chelsea, excluding shoot-outs, with this being his first failure to score from the spot for the Blues since Boxing Day 2020.
But Pulisic swept in from Marcos Alonso's cross to win it. The United States international has been directly involved in 10 goals in 32 appearances for Chelsea across all competitions this term (seven goals, three assists), matching his tally from last season when he made 43 appearances.
Burnley 1-0 Wolves: Clarets out of the bottom three
Burnley claimed a second win on the bounce to lift themselves above Everton and move out of the relegation zone.
They have now won three home Premier League games in a row for the first time since a run of five between December 2016 and January 2017, and that is the same number of victories as they managed across the 26 games beforehand.
Indeed, Burnley have picked up seven points in their three Premier League games under Mike Jackson (W2 D1), the same number of points as Sean Dyche picked up during his final eight league games at the club (W2 D1 L5).
Wolves, meanwhile, have now suffered more defeats in their last five away league games (four) than they had in their first 12 on the road this season (W7 D2 L3).
Matej Vydra grabbed Burnley's winner. Four of his eight top-flight goals for the Clarets have been ones to claim three points.
Brighton and Hove Albion 2-2 Southampton: Ward-Prowse closes on free-kick record
James Ward-Prowse scored both of Southampton's goals as they came from behind to rescue a point in the south coast derby against Southampton.
Despite scoring as many goals on Sunday as they did in their previous seven home Premier League matches, Brighton failed to win a game in which they led by at least two goals for just a third time in the competition (P23 W20 D2 L1), having won each of their previous 13 such matches.
But after an own goal put Brighton further ahead, Ward-Prowse's excellent free-kick halved the deficit. He has now scored 14 direct free-kick goals in the top flight, just four shy of David Beckham's record, while only the Manchester United great and Laurent Robert (both five) have netted more free-kicks in a single season.
Ward-Prowse doubled his tally and restored parity with another long-range effort, and 44 per cent of his league goals for the Saints have come from outside the box (17/39).
Liverpool 2-0 Everton: Origi strikes again to give Toffees the Blues
It took Liverpool until the 62nd minute to break the deadlock at Anfield, though they were arguably fortunate not to have conceded a penalty not long before.
Nevertheless, Liverpool's dominance finally told as Everton's back-to-the-wall display was broken – Andy Robertson heading in before Origi scored late on. The striker has now netted six times in nine league appearances against Everton, scoring once every 62 minutes on average.
Liverpool have lost just one of their last 23 Premier League games against Everton (W10 D12), completing the league double over their neighbours for the first time since 2016-17. They now have 79 points, 50 more than Everton, which is the joint-largest margin they have held in the competition (along with the 2019-20 season).
Everton will end the day in the relegation zone for the first time since December 2019 (also after a derby defeat at Anfield), while this is the furthest into a season, after 32 games or more, the Toffees have found themselves in the bottom three since 1998-99.
They have lost 11 of their last 12 Premier League away games (D1), including each of the last seven in a row. It is their longest run of consecutive away defeats since a run of eight between April and October 1994.
Origi has now scored 11 goals as a substitute in the Premier League, the outright most by a Liverpool player, overtaking Daniel Sturridge's 10.
Liverpool recorded a possession figure of 82.7 per cent against Everton – only Man City (83 per cent v Swansea City in April 2018) have recorded a higher such figure in a Premier League game since Opta started collecting this data (2003-04).
Frank praises Brentford's pressing, sees no tactical revamp with Toney departure
Thomas Frank heaped praise on Brentford's pressing following their 3-1 victory over Southampton on Saturday.
Bryan Mbeumo scored twice from Brentford's forwards forcing the Southampton backline into errors as the Bees earned their second Premier League win of the season.
This did not go unnoticed by Frank, who believes his side rank as one of the best in the league when it comes to that specific aspect.
He told BBC Sport: "They made errors because we pressed them unbelievably well. I think we are one of the best teams to do the high pressure in the Premier League.
"The players are so committed and that is the reason why we capitalised on errors from Southampton.”
Despite the departure of Ivan Toney to Al-Ahli, Frank does not think their style of play will have to be restructured too much, with both Mbuemo and Yoane Wissa enjoying productive starts to the season in his absence.
Frank said: “Ivan is a fantastic player, I'd love to have him in the team but he has his own journey and is going elsewhere.
"Our style of play hasn't changed. Wissa and Ivan are different players but the style doesn't change.”
Southampton boss Russell Martin was frustrated with his side’s mistakes at crucial moments, believing their performance was far better than the scoreline suggested.
He said to the BBC: “We made two mistakes that we were punished for, which is frustrating and disappointing.
"I saw lots of good things to feel positive about. I feel a lot better this week than I did after the Nottingham Forest game.”
Guardiola has 'no words' for hat-trick hero Haaland
Pep Guardiola was lost for words to describe Erling Haaland after his eighth Premier League hat-trick fired Manchester City to a 3-1 victory over West Ham.
Having scored a treble to help City claim a 4-1 win over Ipswich Town on matchday two, Haaland did likewise on Saturday to keep them perfect as they edged out the Hammers at the London Stadium.
Haaland's seven goals this season are the most any player has ever netted in the first three matches of a Premier League campaign, while only Sergio Aguero (12), Alan Shearer (11) and Robbie Fowler (nine) have ever helped themselves to more match balls in the competition.
Across English football's top four tiers, he is also the first player to score two hat-tricks in a team's first three games of a league season since Bradford City's Paul Jewell in 1994-95.
The Norwegian has now scored more than once in 26% of his Premier League matches (18/69, eight hat-tricks, 10 braces), leaving Guardiola in disbelief.
"There are no words for him," Guardiola told BBC Sport.
"All we can do is make him play better and better and give him as many balls as possible into the box. It's what we have to do. We are there and we added quality.
"This is a team. When you have to run backward, no one asks who has to do it. Everyone has to. When we see Erling doing that, it is fantastic."
Haaland himself, meanwhile, believes having an extended pre-season due to Norway missing out on Euro 2024 has helped him start the season in peak condition.
"I feel good. I feel energised. I had a long vacation and a long pre-season. I'm feeling good," Haaland told City's website.
"The years here have gone quick and it's been going like, 'bam bam bam', now I have a little bit of rest in my body and my feet. I feel really good now and I'm ready for more.
"I feel more refreshed and more energised. So when you do that you can practice on things you want to become better at in training. I feel good. I want to become better. I'm happy."
City sit top of the early-season table with nine points from nine available and saw last season's runners-up Arsenal slip up on Saturday, drawing 1-1 with Brighton and Hove Albion.
Haaland, though, feels it is too early to think about the title race, adding: "They [City's rivals] haven't slipped up yet. Three games, nine points. This is a great start.
"But let's not think too far ahead, because there’s potentially 70 games left this season. Let's breathe a bit and take it game by game."
Lopetegui rues missed opportunity as West Ham lose to Man City
West Ham manager Julen Lopetegui was not encouraged by the performance of his team despite losing 3-1 at home to Manchester City in their third league game.
“It is true that City is one of the best teams around the world for sure… but it is also true too that in the second half we have been very close to a draw,” he said speaking to BBC Match of the Day.
“I think we have played one very good second half. The start has been very good for us too.”
West Ham threatened for extended periods of the match and had chances to level the match at 2-1 down, with the best coming from Mohammed Kudus as he smashed a shot against the bar in the second half.
They also started the game brightly before going a goal down inside 10 minutes.
“In my mind we started very well, being aggressive,” said Lopetegui.
“We know in this plan normally they have initiative, it’s very difficult to not concede initiative then. That’s why you have to do a lot of very good things to overcome them.
“In the second half we had chances, I think we kept the ball much more, much more, and didn't concede a lot of chances."
But the hosts were ultimately undone by the brilliant finishing of Erling Haaland, who scored his second hat-trick in as many matches.
“He is one of the best players in the world, that's why he plays for Manchester City,” he said.
“You have to compete with these kind of players. City has the power and the quality to create chances.”
But ultimately, he was left frustrated at the sense of a missed opportunity and that his team were unable to earn themselves a draw that hadn’t seemed implausible during the match.
“Today I think the first goal was a pity for us but I’ve said it. I was happy with the performance think we were able to draw but again they damage us,” he said.
“Against this kind of team, if you make a mistake they don’t forgive. This is the difference they have… A little mistake they punish you, they punish us.
“We have to improve, to know to compete against this kind of team to be close to perfection.
“Don't make mistakes, be calm, defend well… we have quality players too.”
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