The visitors had been below par for much of the match, Paul Scholes' early opener giving way to a late Grant Holt equalizer that the home fans thought had secured a point.
United made a perfect start when Scholes nodded home from close range in the 8th minute, having made a typical late run into the area, but the Canaries eventually roared back into life in an even first half with chances at both ends.
The visiting side seemed to have surrendered two points when Grant Holt netted a fine equalizer late on but Giggs buried a close-range chance at the death to keep his side within two points of leader Manchester City.
Paul Lambert made seven changes from the side that tumbled out of the FA Cup at the hands of Leicester, with vice-captain Russell Martin a headline absentee and Steve Morison on the bench in favor of Grant Holt and Simeon Jackson up front.
For United, the big news was Giggs starting to make his 900th career appearance for the Red Devils. Joining him in the first XI was fellow veteran Paul Scholes, but Wayne Rooney had not recovered from a throat infection to take part.
Norwich opened brightly with some quick crosses but United quickly settled down and broke through early. Nani, already looking dangerous, floated a reasonable but not fatal cross into the area. The home team failed to deal with it and Scholes was waiting at the far post to deposit it simply for the lead.
United could and perhaps should have had a second a few minutes later when a ball was cut back for Danny Welbeck in space close to goal, but the young striker’s low shot was well saved by John Ruddy.
Having been fairly poor for nearly 20 minutes, Norwich woke up somewhat with a period of attacking pressure but none of the decent crosses coming in were able to find the head of Holt.
The home side's quality going forward seemed inconsistent but it nearly carved out an equalizer when Kyle Naughton’s delightful lobbed through pass found an onrushing Anthony Pilkington in the area. David de Gea blocked smartly with his foot to deny the winger.
The two sides began to trade blows in an increasingly exciting match. First Welbeck and Javier Hernandez teamed up delightfully again to put the Mexican through for a low shot, but Ruddy dropped well once more to keep it out.
Then, at the other end, Norwich countered with an excellent flowing move on the right. Pilkington’s left-footed cross swung in towards the onrushing Holt, whose header across the face of goal was intercepted well by De Gea.
Upon resumption the game continued at a much slower pace, nearly an hour having passed before the first significant shot of the second period arrived. Bradley Johnson received the ball from 20 yards out and swiped an effort low past the right post, though it never looked overly threatening.
United should perhaps have gone two up after 63 minutes when Welbeck found his way through the Norwich back line. With little time to move, he dumped the ball out of Ruddy’s reach, but Zak Whitbread got back to clear.
The Canaries started to go more gung-ho in search of an equalizer, turning to winger Elliott Bennett and forward Aaron Wilbraham to make the breakthrough.
Fellow substitute Hoolahan spurned a good chance with 20 minutes to go when he found himself in space just outside the box and had a moment to line up a left-footed shot, but he struck over.
Giggs finally sprung into life a moment later when Phil Jones delivered a fantastic cross coming forward from the right back position. The Welshman got into position to receive it and flicked a header out via the crossbar.
Norwich kept coming, Wilbraham advancing to produce a scintillating long-range shot matched only by De Gea’s brilliant leaping save, but just moments later the Spaniard was beaten as Holt produced a wonderful equalizer.
The striker received a cross on the turn under pressure from the defense, shooting left footed as he wheeled around and buried it past the helpless goalkeeper to reward the home team's determination.
Welbeck, though, should have restored United’s lead straight after. Norwich, in its elation, was caught short at the back when Giggs turned and crossed delicately to the far post. The young forward completely mistimed his header and the chance was gone.
Heroics from Ruddy, saving again from Welbeck, seemed to have secured a point but it was Giggs who had the last laugh, converting a great cross from Young at point-blank range to put the icing on the cake of a landmark day.
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