Owen decides derby in 96th minute
United led three times through Wayne Rooney and two Darren Fletcher headers and City fought back on each occasion with a goal from Gareth Barry and two from Craig Bellamy, the second coming in the final minute of normal time.
The day's big London derby was not quite so dramatic as Chelsea made it six league wins out of six with a 3-0 victory over Tottenham Hotspur who have lost two in a row after winning their first four.
Louis Saha scored twice as Everton beat Blackburn Rovers 3-0 and Wolverhampton Wanderers defeated Fulham 2-1.
The results left Chelsea clear at the top with a maximum 18 points. Manchester United have 15 with City, who had won their first four league games, on 12 alongside Liverpool, Spurs and Aston Villa.
The Old Trafford clash between the champions and a big-spending City side with great expectations was one of the most eagerly awaited for years and more than lived up to its billing.
United got off to a flyer when Rooney made room cleverly to score after two minutes but City equalised when former United striker Carlos Tevez, roundly barracked by the home fans, robbed United goalkeeper Ben Foster and set up Barry to score with a crisp finish.
Fletcher headed in a Ryan Giggs cross in the 49th minute but the lead lasted only three minutes as City broke and Bellamy cut in to unleash a superb rising shot into the top corner.
Shay Given produced three good saves to deny Dimitar Berbatov and Giggs, who was on mesmerising form in his 30th Manchester derby, but he was beaten by another Fletcher header after 80 minutes.
A dreadful blunder by Rio Ferdinand then let in Bellamy, who rounded Foster to score from a tight angle in the 90th minute.
United were not done, though. With City manager Mark Hughes screaming for the final whistle, Giggs split the visiting defence with a perfectly-weighted pass for former Liverpool striker Owen to toe in the winner.
"We won one of the best Manchester derbies," United manager Alex Ferguson told reporters. "We have a neighbour and sometimes neighbours are noisy, but what can you do?
"Our players showed their playing power and that's the best answer of all."
Tottenham, without a win at Stamford Bridge for almost 20 years, started well but fell behind after 32 minutes to a rare goal by fullback Ashley Cole.
Spurs had a strong penalty claim turned down and Michael Ballack bundled in the second before Didier Drogba killed the game with the third goal after 63 minutes.