The evergreen Giggs grabbed the only goal of a tight game at Upton Park just past the hour mark as fellow veteran Edwin van der Sar set a new record in goal.
West Ham matched the title favourites for long periods, with England new boy Carlton Cole having his team's best chance in the first half as his attempted chip was plucked out of the air by Van der Sar after he had been sent clear.
At the opposite end, Robert Green produced a smart reaction save after Cristiano Ronaldo had turned Paul Scholes' wayward shot back towards goal.
In the 34th minute, Van der Sar set a British league record for the longest run without conceding a goal and he was never seriously tested by the Hammers thereafter.
The reigning champions were not at their best, and struggled to create chances until a moment of magic from skipper Giggs settled the contest.
Scholes swept a fine ball out to the left flank on 62 minutes and Giggs cut inside, jinking past two defenders before curling a right-footed shot beyond Green.
Late Hammers pressure failed to yield an equaliser as the Red Devils returned to the top of the table after being temporarily displaced by Liverpool on Saturday.