The Welshman's 62nd-minute winner enabled United to leapfrog Liverpool into top spot on an afternoon when Edwin van der Sar also made it 1,212 minutes without conceding a goal, to break Chris Woods' British goalkeeping record.
With just one defeat in 22 matches in all competitions, Sir Alex Ferguson's side had come into this contest on a run of seven straight Premier League victories.
Indeed, they had not lost a game or conceded a goal in the top-flight since 8 November, when Samir Nasri fired Arsenal to victory at The Emirates, a dozen Premiership games ago.
Following last week's victory over Everton, the World Club Champions made three changes as that man Giggs, Rafael and Paul Scholes came in for Gary Neville (virus) and substitutes Ji-Sung Park and Darren Fletcher.
Unbeaten in eight matches in all competitions, West Ham United had been doing quite nicely themselves and, following their goalless draw at Arsenal last Saturday, Gianfranco Zola's in-form eighth-placed side were unchanged.
And with Wednesday's midweek clash with Spain looming, another Italian coach - Fabio Capello - was at Upton Park, too, to run his eye over the called-up Robert Green, Matthew Upson and Carlton Cole plus ex-Hammers Rio Ferdinand and Michael Carrick.
Certainly it was the east-enders that enjoyed the best of the first half and, with the minutes ticking down to that remarkable resistance record, van der Sar had to be on his toes to stop Lucas Neill's low 18-yarder, before holding Cole's cheeky chip after the confidence-charged Hammers striker had out-muscled Ferdinand inside the United area.
And on 25 minutes, Jack Collison's bulldozing run into the box almost carved out another opening for Cole but, with his back to goal, he was ambushed by a pack of defenders and the chance was lost.
With the tough-tackling Scott Parker, Upson and the impressive James Collins forming an equally solid shield in front of Green, the visitors found themselves continually frustrated in the opening period.
Despite forcing seven first-half corners, the closest United came to breaking the deadlock was when Giggs' clever flag kick found Scholes, whose blistering 20-yarder looped off Collins before being palmed over by the alert Green, while Cristiano Ronaldo also sent a bullet-header wastefully wide from another one of the Welsh wizard's crosses.
West Ham started the second half in mean mood, too, and Neill again had van der Sar diving at full length to save another 18-yarder as the determined Dutchman moved himself closer to Woods' record.
In reply, former Hammers hero, Carlos Tevez, nodded Ronaldo's well-flighted, free-kick wide, before Neill received referee Phil Dowd's 50th yellow card of the campaign for upending the Portuguese playmaker.
Nemanja Vidic then became offender number 51 for hauling down the breaking Cole, who endured more agony on 62 minutes, when he rashly dived in on Giggs out on the left flank and, having just collected from Scholes, the now unmarked Welshman then ghosted past Neill, before firing a low 15-yarder through a pack of bodies to break the deadlock.
Zola responded by replacing Mark Noble with £9million signing Savio Nsereko for the final quarter-hour but, by now, there was no way past the United defence, whose place at the top of table was assured alongside van der Sar's clean-sheet record.