Nade, a free-transfer signing from Troyes in the summer, scored the winner five minutes from the break - his first Premiership goal for the Blades.
Jagielka then stepped into the limelight by playing the final 30 minutes in goal, after Paddy Kenny had sustained a groin injury and to a raucous backdrop at Bramall Lane.
It was Jagielka's third position of the match - because he started out at centre-half, then switched to midfield when Mikele Leigertwood was injured before eventually stepping between the posts.
But it was not just Jagielka who produced a heroic performance - every single United player covered themselves in glory.
The victory was United's first over Arsenal in the league for 33 years and 14 matches, ending the Gunners' six-game unbeaten run coming into this clash.
Remarkably, it came with a 'second-string' side - because it was apparent from Warnock's team line-up he had one eye on the New Year's Day match at Middlesbrough.
Warnock made six changes - leaving four of his key players on the bench in Claude Davis, Rob Hulse, Michael Tonge and Danny Webber.
In attack, Warnock gambled on 22-year-old Nade and 20-year-old Colin Kazim-Richards - adopting a youth policy akin to that of Arsene Wenger, who made four changes of his own because of injury and illness.
Wenger headed north without nine of his big-name stars in Thierry Henry, Freddie Ljungberg, Alexander Hleb, Theo Walcott, Emmanuel Adebayor, Johan Djourou, William Gallas, Emmanuel Eboue and Abou Diaby.
There are not many clubs who could cope with such a casualty list.
So it proved too; yet Arsenal were swiftly out of the blocks, dominating the opening exchanges.
In the fifth minute Kenny was forced into a flying save to turn aside a delightful 18-yard effort from Tomas Rosicky with the outside of his right boot.
Captain Gilberto then planted a free header into the ground from inside the six-yard box in meeting a Robin van Persie corner, the ball bouncing over the bar.
The Blades weathered the early storm, though, and steadily grew in confidence and composure as the half wore on.
They rattled Arsenal with their physical aggression and, other than another Kenny save from Jeremie Aliadiere, were rarely troubled.
Given such a young duo up front, United struggled to carve out opportunities of their own.
They perhaps should have taken the lead midway through the half when an unmarked Alan Quinn gave Jens Lehmann a comfortable save with a side-foot effort from 14 yards.
But Warnock's side did take the one chance that mattered five minutes from the break, and in some style.
Davis, who had replaced Leigertwood in the 26th minute after the midfielder had been fouled by a crunching yellow-card tackle from Rosicky, combined with Quinn to set up Nade.
But several yards in from the left-hand touchline, and with his back to goal, the young Frenchman still had a lot of work to do.
However, he showed superb strength to shrug off Kolo Toure before curling a superb shot past Lehmann who had advanced to the edge of the area.
It then became a goalkeeping tale as 12 minutes into the second half Kenny appeared to sustain a groin injury in taking a goal-kick as he pulled up sharply in pain.
Despite lengthy treatment and a heavy strapping, it was obvious the Republic of Ireland international could not continue.
With no substitute goalkeeper on the bench - as is Warnock's policy - it led to Tonge replacing Kenny on the hour, and Jagielka taking over the gloves, not for the first time in his career.
What followed was an astonishingly resilient 30 minutes as United defended to a man, doing anything and everything to protect Jagielka.
Their efforts were not in vain either, because Jagielka was barely tested - while every catch and fisted clearance was cheered to the rafters by the majority of a 32,000 crowd.
He made just one save, in the 85th minute tipping over the bar a bouncing shot into the turf from van Persie which appeared to be going high anyway.
Despite five minutes of injury time, Jagielka and United held on to give Warnock a famous victory over a man he most admires.