Manchester City manager Pep Guardiola said Sergio Aguero is "an authentic legend of this club" after the Argentine's four-goal haul in the Premier League rout of Leicester City.
The win extended City's Premier League lead to 16 points while Harry Kane netted again as Tottenham Hotspur beat north-London rivals Arsenal.
Socceroos goalkeeper Mat Ryan was the hero for Brighton & Hove Albion in their draw at Stoke City.
After a sluggish first half in the early kickoff 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 manager 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.
"Sergio is like this, he has a special talent in the box. He is clinical. We are so happy, we need his goals," Guardiola said.
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 teasing cross in the 48th minute and collected another pass from the Belgian to fire through Kasper Schmeichel's attempted save.
The forward completed his hat-trick with a delicate chip before adding a fourth with an unstoppable, dipping drive which crashed in off the underside of the crossbar.
"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 - joined 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 Evertonn's straightforward 3-1 win over Crystal Palace at Goodison Park.
The Toffees are ninth and the only negative was Luka Milivojevic's late consolation for Palace from the penalty spot.
In south Wales, 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 and ended a run of three league games without victory with a 2-0 win over Watford thanks to goals from Javier Hernandez and Marko Arnautovic.
Stoke City drew 1-1 with Brighton after Xherdan Shaqiri cancelled out Jose Izquierdo's brilliant opener for the visitors.
Charlie Adam had a 90th-minute penalty saved by Ryan to leave Stoke in the relegation zone.