United's first victory at Anfield since 2016 gave under-fire boss Ruben Amorim a much-needed boost.
Arsenal's stingy defence kept the Gunners top with a 1-0 win at Fulham, while Erling Haaland was again Manchester City's match-winner with a double to beat Everton 2-0.
AFP Sport looks at three talking points from the Premier League weekend:
Liverpool crisis deepens
Liverpool have suffered four straight defeats for the first time since November 2014, raising serious questions about their summer spending spree.
The vast majority of a near £450 million spend in the transfer market was focused on adding extra firepower to the Reds' attack.
But club record signing Alexander Isak and Florian Wirtz are yet to score a Premier League goal for Liverpool, while Arne Slot's men are suddenly wide open at the back.
Liverpool conceded just five times in Slot's first 12 games last season as he took a more conservative approach in his early days as Jurgen Klopp's successor.
At the same stage this season, the English champions have shipped 17 goals.
Slot has been keen to use his wealth of attacking options. For the final half hour against United, he played with five forwards.
However, that lack of balance was exposed as, just six minutes after Cody Gakpo had cancelled out Bryan Mbeumo's opener, Harry Maguire was left completely unmarked to head in Bruno Fernandes' cross.
"I think we conceded a very sloppy second goal," said Liverpool captain Virgil van Dijk.
"We worked so hard to get back into the game, and we created great opportunities to score the winner, but if you concede a second goal like that, that is the disappointing part."
1-0 to the Arsenal
The Gunners have a history of success built on solid defensive foundations.
Two league titles won under George Graham in 1989 and 1991 gave birth to the chant '1-0 to the Arsenal', such was the frequency of that scoreline at the old Highbury.
Yet, Mikel Arteta's current crop have proved even more difficult to breach in setting a new club record after conceding just three times in their opening 11 games of the season in all competitions.
For the second consecutive game, Arsenal did not even concede a single shot on target in grinding out a 1-0 win at Fulham to retake top spot.
"The level of organisation I'm very pleased with, but it's more about the mindset and the willingness to do it," said Arteta.
"The way our front line chases the ball, puts people under pressure, creates chaos there, it's phenomenal."
Once again, Arsenal required a set-piece to get the only goal as Leandro Trossard turned in Gabriel Magalhaes' flick-on from a corner.
But they do not need to be prolific in front of goal if they continue to concede at a historically low level.
Black Cats buck promoted trend
Sunderland were languishing in English football's third tier just over three years ago.
Now they are looking down on their Saudi-backed local rivals Newcastle after a dream start to their Premier League return.
The Black Cats have matched their best-ever start to a Premier League campaign with 14 points from eight games after beating Wolves 2-0 at the Stadium of Light.
For the past two seasons, all three promoted clubs from the Championship have sunk straight back to the second tier.
But a squad overhaul with 14 new signings has put Regis Le Bris' side in position to end that trend.
Relegated trio last season, Southampton, Leicester and Ipswich managed just 14 points between them after eight matches last season.
Sunderland's points tally is the best from a promoted side since Wolves in 2018/19.
