The champions were comprehensively outplayed and beaten by their rivals at the Etihad Stadium, with Sergio Aguero netting twice either side of a Yaya Toure goal before Samir Nasri also got in on the act.
Wayne Rooney's fantastic free-kick in the 87th minute made him the top scorer in Manchester derbies with 11 goals, but it was scant consolation for David Moyes' men.
City are two points behind joint leaders Arsenal and Tottenham after five games played, and three above United who lie eighth in the early table.
The visitors were missing Robin van Persie due to a groin strain, although David Moyes is hopeful the injury will only keep the Dutchman out for one match. Danny Welbeck and Ashley Young started against City, with Shinji Kagawa benched. Manuel Pellegrini preferred Alvaro Negredo to Edin Dzeko in attack.
The physical style of Negredo and City captain Vincent Kompany upset United almost from the get-go and after 16 minutes, the hosts forged ahead.
Poor defending from United down the right led to the opener. Chris Smalling was left one-on-one with Nasri, and Antonio Valencia failed to track back quickly enough as Aleksandar Kolarov passed his City team-mate on the overlap. The Serbian crossed from the left, and Aguero netted with a stylish volley.
Rooney was booked in the first half for persistent fouling as Kompany won their personal duel.
One minute of added-on time at the end of the first half proved crucial for City as they doubled their lead. Pablo Zabaleta won a corner off Young and from Nasri's set piece, Negredo headed down for Toure to force the ball home.
Two minutes after the interval, a third City goal arrived. Negredo spun Nemanja Vidic on the left side of the area and knocked a simple cross over for Aguero - who had not been tracked - to net his second goal of the game.
Kompany made a key contribution as Samir Nasri scored a fourth goal in the 50th minute. Jesus Navas crossed from the right and Kompany drew away the centre-backs, allowing Nasri to volley home at the far post.
Tom Cleverley was introduced by Moyes for Young, and United improved. Valencia had a penalty appeal turned down after tussling with Kolarov on the right side of the area.
Patrice Evra headed against the post in the 81st minute and finally United did get on the scoresheet when Rooney flighted home a wonderful free-kick three minutes from time.
City and United move on to Capital One Cup assignments in midweek at home to Wigan and Liverpool respectively. City's next league game is away to Aston Villa next Saturday, when United host West Brom.