Manchester City manager Pep Guardiola said Sergio Aguero is "an authentic legend of this club" after the Argentine's four-goal haul in the English Premier League rout of Leicester City.
The win extended City's Premier League lead to 16 points while Harry Kane netted again as Tottenham beat North London rivals Arsenal.
After a sluggish first half in front of a Premier League record crowd of 83,222 at Wembley, Kane jumped highest to head home his seventh derby goal in seven games and 23rd in the league this season.
Spurs, who would have won by a greater margin but for an inspired performance from goalkeeper Petr Cech, climbed two places to third while Arsenal sit six points adrift of Liverpool in fourth and Juergen Klopp's side have a game in hand.
"I am so happy to win," Spurs coach Mauricio Pochettino said. "We have had three massive games against [Manchester] United, Liverpool and Arsenal and seven points is good."
At the Etihad Stadium, Aguero and the brilliant Kevin De Bruyne, who contributed three assists, were in inspired form as City blew away Leicester City in the second half to seal a 5-1 result — their 23rd league victory from 27 games.
After Raheem Sterling and Jamie Vardy exchanged first-half goals, Aguero took over and effectively ended the game with two strikes within eight minutes after the break.
He converted De Bruyne's cross in the 48th minute and collected another pass from him to fire through Kasper Schmeichel's attempted save.
The forward completed his hat-trick with a delicate chip before driving in a fourth.
"I don't know [which was my favourite goal] — maybe the last one because it's a long time since I scored from outside the box," Aguero said.
The 29-year-old now has 21 league goals this season and became only the fourth player — with Kane, Thierry Henry and Alan Shearer — to score more than 20 times in four successive Premier League campaigns.
Gylfi Sigurdsson, Oumar Niasse and Tom Davies were on target in Everton's straightforward 3-1 win over Crystal Palace at Goodison Park.
Swansea City registered a third Premier League victory in four matches, with Ki Sung-yueng's late strike lifting them to 15th after a tense 1-0 victory over Burnley.
West Ham United climbed five points above the relegation zone with a 2-0 win over Watford.
Brighton drew 1-1 at Stoke City thanks to Socceroos keeper Mat Ryan saving a 90th-minute penalty from Charlie Adam.