An unfortunate own goal from Manuel Almunia - the ball bouncing back off the post and in off the Spaniard - put City in front but Robin van Persie equalised just after the hour mark.
But Craig Bellamy put City back in front and then goals from Emmanuel Adebayor - against his old club - and Shaun Wright-Phillips sealed a superb win for Mark Hughes's side, though Tomas Rosicky pulled another back late on.
Hughes would not be drawn on City's chances of winning the title this season, but acknowledged the importance of today's match.
'It was important we made a mark today and we did that, we were good value for the win,' said Hughes. 'Now we have to sustain that performance from now until the end of the season.'
Tottenham Hotspur could not make it five wins from five as they fell to a 3-1 defeat against the champions at White Hart Lane.
In an exciting and open game, the home side took a first minute lead through an overhead kick from in-form striker Jermaine Defoe.
But the champions quickly asserted themselves and they equalised after 25 minutes through a superb free kick from the veteran Ryan Giggs.
United turned the screw thereafter with goals from Brazilian midfielder Anderson and Wayne Rooney. Despite the sending-off of Paul Scholes on the hour mark, Utd had little difficulty in securing the victory.
Elsewhere, Liverpool moved into fifth place with a confident 4-0 victory over Burnley at Anfield, with Yossi Benayoun scoring a hat-trick.
And on a day of 31 Premier League goals, there were also wins for Sunderland, Blackburn Rovers, Bolton Wanderers and Wigan Athletic.