Elsewhere, Everton left it late to rescue a point in a 1-1 draw with Leicester City, Newcastle won at home again - 1-0 versus Crystal Palace - and managerless Burnley boosted their survival bid with a 2-0 triumph over Southampton.
Here, Sports Mole picks its Premier League Team of the Week for the latest round of fixtures.
One Burnley stalwart in Sean Dyche may have left the club, but number one goalkeeper Nick Pope is going nowhere, and the England international played his part in the crucial win over Southampton, making three stops - including a brilliant reaction save from Che Adams - to post a welcome clean sheet.
Pope is the first of three representatives in a Burnley-heavy defence this week, with Connor Roberts opening the scoring in some style on his weaker foot on Thursday night - curling a delightful effort beyond the reach of Fraser Forster - while he also made two blocks and two key passes in an assured all-around display.
The Turf Moor faithful were treated to some stellar showings from their rearguard members against Southampton, and Nathan Collins typified a classic Burnley display - doubling his side's lead with an accurate header while also winning all eight of his duels on the ground and in the air.
In contrast, defending was not on the menu for either side at Stamford Bridge during Arsenal's London derby with Chelsea, but Gabriel Magalhaes was a calm and composed figure at the back, posting six clearances, four tackles and winning four of his five ground duels during a priceless win.
Kyle Walker's absence from the Man City squad has seen Joao Cancelo shift back to his right-back role, but the Portuguese is just as confident on the left and has been moved here for the purposes of this XI after registering five tackles, four interceptions and two key passes for the reigning champions against Brighton.
There must have been at least a few Manchester United fans who could not resist a round of applause for Thiago Alcantara, who was here, there and everywhere for the Reds on Tuesday night, posting a 96% pass accuracy, completing all three of his dribbles successfully and playing three key passes in a midfield masterclass.
Thiago's remarkable performance came without a goal or assist, while Josh Brownhill - the fourth Burnley name in our XI - set up both of his side's goals in the pivotal win over Southampton, as well as making five key passes and winning all three of his ground duels for the managerless Clarets.
It comes as no surprise to see Kevin De Bruyne weave his way into the XI just like he weaved his way through the Brighton midfield in midweek, as the Belgian recorded the assist for Bernardo Silva's goal and had a huge part to play in Riyad Mahrez's opener against the stubborn Seagulls.
Liverpool boss Jurgen Klopp recently insisted that Mohamed Salah would soon find his shooting boots, and the Egyptian picked an ideal game to reignite his Golden Boot charge, bagging two goals against the Red Devils - the first of which came after a sublime first touch - following his early assist for Luis Diaz's opener at Anfield.
It would have been easy to select a full Liverpool frontline this week given Diaz's contributions, but it was impossible to overlook Eddie Nketiah's star performance against Chelsea. The former Blues youngster took all of 50 minutes to equal Alexandre Lacazette's open play Premier League goal tally for the season - taking both of his chances like a true striker should - and he has surely cemented his spot in the Arsenal XI for the remainder of the season.
Nketiah just edged Diaz out for a spot in this team, but Salah is joined by a familiar face in the forward line. While Sadio Mane also registered a calmly-taken goal of his own versus Man United, the Senegal international's assist for Salah was a thing of beauty, and he seemingly has unfinished business at Anfield.
Sports Mole's Premier League Team of the Week (4-3-3): Pope; Roberts, Collins, Gabriel, Cancelo; Thiago, Brownhill, De Bruyne; Salah, Nketiah, Mane