Emotional Norris wins epic rain-hit British Grand Prix
The 25-year-old Briton made the most of series leader Piastri's mid-race misfortune, when he was given a 10-second penalty for slowing excessively while leading behind the safety car, to finish 6.8112 seconds clear.
It was his first home win, his fourth win of the year and the eighth of his career, lifting him within eight points of the Australian.
"Thank you, McLaren, thanks everyone," said Norris.
"This is beautiful. Winning at home. This is a dream."
Nico Hulkenberg finished a stirring third for Sauber to claim the first podium appearance of his long career after 239 races.
"It feels good," the veteran German said.
"A long time coming! But we had it in us and I had it in me somewhere. It’s pretty surreal. All a bit crazy now."
Piastri was careful not to express his disappointment at the time penalty verdict.
"I want to congratulate Nico," he said.
"That’s the best story of the day – but I don’t want to say much else to avoid getting into trouble."
Norris became the 13th different home winner of the British race.
Lewis Hamilton took fourth for Ferrari ahead of Red Bull's four-time champion Max Verstappen.
In an epic event run in extreme and changeable weather conditions, Pierre Gasly was sixth for Alpine, ahead of Aston Martin's Lance Stroll, Williams' Alex Albon, two-time champion Fernando Alonso in the second Aston Martin and Mercedes’ George Russell.
On a cool and wet summer's day in central England, the race began as the sun slanted through the clouds following torrential rain, Verstappen leading a controlled formation lap behind the safety car.
In F1's 75th anniversary year, it was the 1,173rd race since the inaugural world championship event at Silverstone on May 13, 1950, and with the field so closely-packed few races had been more keenly anticipated.
Russell and Leclerc gambled on switching to slick tyres before the start as Verstappen led the opening lap from his 44th pole ahead of Piastri, Norris and Hamilton.
RB's’ Liam Lawson went off at Stowe on lap one, triggering a virtual safety car (VSC), and Franco Colapinto retired his Alpine after stalling in the pit-lane.
The race re-started on lap five with Piastri hounding Verstappen before a second VSC intervention when Gabriel Bortoleto abandoned his Sauber. It was stop-go stuff with everyone waiting for more rain.
After chasing him, Piastri passed Verstappen at Stowe on lap eight to lead. Verstappen then ran off at Becketts and Norris passed him before they all pitted as the rain resumed.
Blinded by spray
Norris suffered a slow stop, giving second, behind Piastri, back to Verstappen, in appalling conditions that prompted another full safety car and wiped out the Australian’s 13-second advantage.
"There's water in my visor, a huge splash and I can’t see," reported Leclerc after bouncing across the grass at Becketts.
Hamilton was also blinded by spray, dropping to eighth, as the field cruised through puddles.
Racing resumed on lap 18 amid plumes of spray before a third full safety car was deployed when RB rookie Isack Hadjar crashed into Antonelli's Mercedes at Copse.
The action re-started on lap 22 with a gripless Verstappen sliding off out of Copse as he spun, after Piastri had braked dramatically in front of him before the safety car peeled in.
After a brief investigation, Piastri was given a 10-second penalty.
By lap 26, and mid-race, Piastri led Norris before the Australian pitted to serve his time penalty, leaving Norris to soak up a memorable win.