Manchester City moved five points clear at the top of the Premier League despite having Rodri sent-off in a fiery 2-0 win over Nottingham Forest on Saturday, while Manchester United snapped their losing streak by beating Burnley 1-0.
Phil Foden and Erling Haaland struck inside the first 15 minutes as City extended their perfect start in the Premier League to six games.
Pep Guardiola's men have now won 20 consecutive home matches in all competitions, but were made to work much harder by Rodri's moment of madness.
The Spaniard grabbed Morgan Gibbs-White around the neck less than 60 seconds into the second-half and could face a costly suspension as a three-game ban would see him miss the Premier League visit to Arsenal next month.
"An exceptional game in the first-half. Exceptional game in the second for our resilience and our work because we played 52 minutes 10 against 11, so it was not easy but we were fantastic," said Guardiola.
"Hopefully Rodri will learn. He has to control his emotions."
City were at their ruthless best early on to seemingly put the game to bed.
Foden smashed home a sweet volley from Kyle Walker's cushioned cross to open the scoring.
City's injury problems handed Matheus Nunes a chance to make his first league start since joining from Wolves and he made a positive impact by setting up the second goal.
Nunes played a neat one-two with Foden before chipping the ball across for Haaland to power home his ninth goal of the season.
The European champions did not appear in any danger until Rodri lost his cool.
Taiwo Awoniyi had Forest's best chance to get back into the game when the in-form Nigerian lifted over under pressure from Ederson.
City, though, restored order as Guardiola switched to a back five to withstand an aerial bombardment from the visitors.
Liverpool can cut City's lead back to two points when they face West Ham on Sunday, as can the winner of the north London derby between Arsenal and Tottenham.
United remain nine points adrift of the leaders, but eased the pressure on Erik ten Hag after three consecutive defeats.
One moment of world class quality from Bruno Fernandes got the Red Devils back to winning ways as the Portuguese volleyed home Jonny Evans' pass just before half-time.
The Red Devils had to survive a few nervy moments at Turf Moor as Zeki Amdouni hit the post in the first-half, but the Clarets remain without a win on their return to the Premier League.
"Today was must-win," said Ten Hag.
"You have to fight and find a turning point. It shows the dressing room is together. They fight together."
Struggling Everton beat Brentford 3-1 to earn their first league win this term and climb out of the relegation zone.
Sean Dyche's side took the lead through Abdoulaye Doucoure's sixth minute strike.
Mathias Jensen equalised for Brentford against the run of play after 28 minutes, but James Tarkowski restored Everton's advantage with a header from Dwight McNeil's corner in the 67th minute.
Substitute Dominic Calvert-Lewin wrapped up Everton's long-awaited three points with a cool finish four minutes later.
Luton picked up their first ever Premier League point but let a huge opportunity slip in a 1-1 draw at home to Wolves.
The visitors at Kenilworth Road were reduced to 10 men when Jean-Ricner Bellegarde saw red on 39 minutes.
Pedro Neto still fired Wolves in front early in the second-half, but Carlton Morris' penalty salved a point for Luton.
Crystal Palace and Fulham remain in the top half after a 0-0 draw at Selhurst Park.
