Also yesterday, Swansea City won 2-0 at Crystal Palace and Tottenham Hotspur beat Cardiff City 1-0. Spurs are level with Arsenal on points, though have an inferior goal difference.
Yaya Toure and Samir Nasri also scored for City at its Etihad Stadium before United striker Wayne Rooney got a late free kick for his record 11th goal in Manchester derbies.
“The way we played is the way I want this team to play,” City manager Manuel Pellegrini told Sky Sports after his first Manchester derby. “We went 4-0 up and Manchester United didn’t have a really clear chance apart from a beautiful free kick by Rooney and one corner.”
United lined up without striker Robin van Persie because of a groin strain and City dominated from the start. Aguero gave the home team a 16th-minute lead with a left-foot volley from the edge of the six-yard area.
Toure made it 2-0 off his knee just before half time after Alvaro Negredo headed on Nasri’s corner.
Two minutes after the break, Aguero converted Negredo’s cross to make it 3-0 and Nasri volleyed in Jesus Navas’s cross from the right three minutes later to put City four goals up.
Substitute Edin Dzeko almost scored a fifth for City, goalkeeper David de Gea smothering the striker’s shot.
Patrice Evra headed against a post for United, then Rooney curled his free kick past goalkeeper Joe Hart three minutes from the end.
“We have been playing irregular in other games, but it is normal in this moment of the season,” Pellegrini said. “This was a high test and the players had a great answer.”
“They started much stronger and quicker,” Moyes said. “We’ll get better, there’s a long season to go. We’ll put this behind us and move on.”
Six of United’s 13 Premier League titles have come after the Red Devils won only two of their opening five matches, according to Opta Sports.
Arsenal and Tottenham have 12 points through five games. Manchester City, Chelsea and Liverpool have 10, followed by Everton (9) and Southampton (8). United, Swansea, Stoke, Hull City and Newcastle United each have seven points.
At the Emirates Stadium, Arsenal’s Theo Walcott was ruled out by illness and Serge Gnabry started his first Premier League game. Midfielder Mesut Ozil made his home debut after a 42 million-pound ($67 million) transfer from Real Madrid and delivered the set-pieces that led to all three goals.
Aaron Ramsey gave Arsenal a fifth-minute lead after goalkeeper Asmir Begovic pushed out Ozil’s free kick.
Geoff Cameron leveled for Stoke 21 minutes later after Marko Arnautovic hit the post, and Per Mertesacker restored the home team’s lead from close range in the 36th minute. Bacary Sagna’s looping header in the 72nd minute closed the scoring.
It was Arsenal’s seventh straight win in all competitions after losing its opening league game to Aston Villa.
“We are in a position where we can focus on improvement in a stable environment,” Arsenal manager Arsene Wenger said in a news conference. “That’s a good basis.”
Paulinho got Tottenham’s winner at Cardiff in stoppage time, leaving the Welsh club in 16th place with five points.
Michu gave Swansea the lead in the second minute at Palace and Nathan Dyer made it 2-0 soon after half time. Palace is one spot above last-place Sunderland, which last night fired manager Paolo Di Canio. The 45-year-old Italian won three of his 13 matches since being appointed in March.
Two days ago, Chelsea beat Fulham 2-0, Liverpool lost 1-0 at home to Southampton, Hull had a 3-2 victory at Newcastle, and Aston Villa won 1-0 at Norwich. West Brom defeated Sunderland 3-0 and West Ham was beaten 3-2 at home by Everton.
To contact the reporter on this story: Peter-Joseph Hegarty in London at firstname.lastname@example.org
To contact the editor responsible for this story: Christopher Elser at email@example.com