The champions had been in danger of falling four points behind leaders Manchester City after Norwich captain Grant Holt had netted a late equaliser.
That had cancelled out Paul Scholes’ goal for United but fellow veteran Giggs was in the right place at the right time two minutes into added time to make sure Sir Alex Ferguson’s side remained within touching distance of their neighbours.
Giggs flicked an early United chance wide at the back post before Scholes opened the scoring in the seventh minute.
It was all too easy as Phil Jones teed Nani up for a cross from the right that Javier Hernandez flicked on to the back post, where Scholes had eluded marker David Fox for a simple headed finish.
United survived an almighty scramble in their own box from a free-kick as Norwich retaliated with a barrage of pressure that included a Holt header that dropped just wide.
David de Gea kept United in front with a fine block to deny Anthony Pilkington from five yards in the 28th minute.
The Norwich winger brought down Kyle Naughton’s pass superbly but the Spain international was able to get in the way of his first-time effort.
Still Norwich attacked but they had John Ruddy to thank for a smart save to deny Hernandez, who had motored into a shooting position via a one-two with Danny Welbeck.
De Gea was then needed to make an even better one at the other end when Holt met Pilkington’s cross from the right with a glancing header that the goalkeeper not only saw in time but also caught.
United went in at half time in the lead but knowing there was much work still to do and Norwich made a change for the second half with playmaker Wes Hoolahan coming on.
Welbeck almost wrapped the game up for United in the 64th minute when his movement in the box allowed him the time and space to loft the ball over Ruddy, but Zak Whitbread had anticipated and was there to hack the ball clear when it landed.
Then Giggs was denied a goal on his milestone match by the crossbar when he met Jones’ cross from the right with a volley that had the beating of Ruddy.
Norwich redoubled their efforts after that but neither Elliott Ward or Holt could direct headers on target and a shout for handball in the box when Hoolahan’s cross hit Patrice Evra on the arm was ignored by referee Andre Marriner.
Norwich had sent on Aaron Wilbraham as their final substitution and the former MK Dons forward forced another diving save from de Gea before Holt finally beat him in the 83rd minute.
De Gea made a powerful punch but the ball was back in the United area within seconds. Whitbread headed the ball on and Holt swivelled to beat Rio Ferdinand before rifling a shot on the turn before Michael Carrick could intervene.
Whitbread then made a brave block to deny Young at the other end and Welbeck then completely missed a free header after Giggs had picked him out in front of goal with a chip.
Welbeck then failed to beat Ruddy from another clear chance as United threw men forward but Giggs had the last word, arriving at the back post to volley in Young’s cross for a stoppage-time winner.