The 22-year-old midfielder, hauled into United's weakened side and making only his fifth start of the season, grabbed the winner in the 41st minute.
More drama followed as keeper Paddy Kenny limped off in the 61st minute with Phil Jagielka taking over in goal, but Warnock's battlers held Arsenal at bay in a nail-biting finish.
Both sides had been decimated by injuries and viral infections. United were without six players while Arsenal, who ran out 3-0 winners against the Blades at the Emirates Stadium in September, were without nine first-team regulars.
The Sheffield side were caught out early on. Jeremie Aliadiere pumped over a curling cross to Julio Baptista who was met with a crunching tackle from Nick Montgomery.
Gunners skipper Gilberto Silva, who has hit a rich vein of form in front of goal, was first to react to a Robin van Persie corner but pulled his downward header wide of the target.
Jagielka then tried his luck from 30 yards, Colin Kazim-Richards almost getting a touch as the ball flashed a fraction wide of the far post.
Midfielder Alan Quinn, in for his injured brother Stephen, then squandered a chance shooting straight at Jens Lehmann from 16 yards after Arsenal failed to clear.
United had to readjust in the 27th minute after Mikele Leigertwood limped off, Claude Davis slotting into the back four as Jagielka pushed into midfield.
And it was Davis who sparked United's goal in the four minutes before half-time. The big defender threaded the ball to Quinn who played a hopeful pass to Nade as Kolo Toure shadowed him.
But the Ivory Coast centre-back made a rare blunder as the ball spun past him and Nade turned quickly to side-foot his low strike past the advancing Lehmann from the edge of the area.
United were in trouble when Kenny suffered a groin injury as he slipped taking a goal kick, the Republic of Ireland international keeper being replaced in goal by the versatile Jagielka.
Quinn powered a long-range strike wide of the far post and, minutes later, he was stopped by Lehmann, the Arsenal keeper smothering his low shot at the foot of the post as United tried to kill off the side from the capital.
Arsenal powered forward in the dying minutes but were closed down quickly. Jagielka punched clear twice and foiled van Persie five minutes from time, tipping his close-range strike over the top.