City's young Englishman Micah Richards shone for City in defense and thwarted Carlos Tevez. Man U was playing without injured Wayne Rooney and suspended Cristiano Ronaldo.
In the second half, United almost tied the score in the 47th when Vidic headed a corner from Ryan Giggs off the crossbar.
Liverpool tied Chelsea, 1-1. Fernando Torres gave Liverpool the lead before Frank Lampard equalized from the penalty spot.
Arsenal was held to a 1-1 to by Blackburn. Arsenal keeper Lens Lehmann made his second major blunder of the season, failing to catch a shot right at him from David Dunn.
Robin van Persie scored on a rebound after Blackburn's American keeper Brad Friedel parried a shot from Eduardo da Silva.
ENGLAND, Premier League Aug. 18-19/Day 3
Portsmouth 3 (Kanu 16, Utaka 30, Taylor 88, pen.) Bolton 1 (Anelka 13)
Birmingham City 0 West Ham United 1 (Noble 70 pen)
Wigan Athletic 3 (Heskey 19 Landzaat 62, pen., Sibierski 69, pen.) Sunderland 0
Fulham (McBride 16) 1 Middlesbrough (Mido 56, Cattermole 88)
Tottenham Hotspur 4 (Malbranque 2, 6 Jenas 14, Bent 79) Derby 0
Reading 1 (Hunt) Everton 0
Newcastle United 0 Aston Villa 0
Manchester City 1 (Geovanni 31) Manchester United 0
Blackburn Rovers 1 (Dunn 72) Arsenal 1 (van Persie 18)
Liverpool 1 (Torres 16) Chelsea (Lampard 62, pen.)