In a cagey game of few chances, Giggs jinked past two West Ham players after 61 minutes before skimming a low shot inside the far post to put the champions two points clear of Liverpool.
United have 56 points from 24 games while Liverpool, who beat Portsmouth 3-2 on Saturday, have 54 from 25.
United's miserly defence was never unduly troubled as they registered a 13th consecutive league clean sheet while goalkeeper Edwin van der Sar made it over 20 hours since he last had to pick the ball out of his net in the league.
"This has been a difficult match for us over the years and this was a great result for us to come away with a win," Dutchman Van der Sar told Sky Sports.
"The defenders are incredible, how they defend, how they clear the ball, it's a team effort."
Arsenal remain a distant fifth with 44 points after drawing 0-0 at north London rivals Tottenham Hotspur despite playing for nearly an hour with 10 men after Emmanuel Eboue was sent off.
Eboue, who also had a goal disallowed, was shown a red card for a sneaky kick at Tottenham's Luca Modric after 36 minutes but the home side, even with Robbie Keane back in the starting line-up, failed to take advantage.
For all their attacking flair, United's surge towards a hat-trick of Premier League titles has been built on rock-like defending. Sunday's victory was their sixth by 1-0 in an eight-match winning sequence in the league.
West Ham had not lost until before Christmas and started confidently against United.
Carlton Cole, who was included in the England squad on Saturday, had the game's first chance when he found a rare gap in United's defence before trying to chip Van der Sar.
At the other end a Paul Scholes shot was re-directed by Cristiano Ronaldo, forcing a fingertip save from West Ham keeper Robert Green.
United were comfortable after the break without really threatening until two of their most experienced players combined to unlock West Ham's defence.
Scholes drilled a perfect crossfield pass to pick out Giggs on the left wing and the Welsh winger cut in, side-stepped past two static West Ham players and threaded a shot into the net.
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