Norris wins wild and wet Miami GP sprint race
Ferrari's Lewis Hamilton finished third while 18-year-old Italian Kimi Antonelli, who had started on pole for Mercedes, finished in tenth.
Antonelli lost his lead at the first turn where Piastri forced him wide and when he returned to the track he was down in fourth.
The race got underway after a 25-minute delay due to heavy rain which had impacted the formation lap.
Ferrari's Charles Leclerc crashed out during the formation lap hitting the wall after aqua-planing.
During the race, Fernando Alonso crashed into the wall after he was clipped by Liam Lawson and Carlos Sainz also crashed.
There was a contact incident in the pit-lane when Red Bull's Max Verstappen pulled out into Antonelli. The Dutchman was penalised 10 points for 'unsafe release' leaving him in 17th place.
Norris, who won the Miami GP last year, came out of the pits just ahead of Piastri and was helped by the race ending under the safety car after the Alonso crash.
"My luck in Miami seems pretty good at the minute, so I'm happy," said Norris.
"The pace was still very good but it's so difficult these races. Do you box early like Lewis, or stay out and hope for a Safety Car. I'd rather this happened tomorrow but I'll take it," he added, after a victory which reduced the gap on Piastri in the drivers' standings from ten to nine points.
Hamilton 'gamble' pays off
After his aggressive start and controlling the race for long stretches, Piastri was frustrated at not having the chance to fight back on the final laps but was turning his focus to Saturday's qualifying.
"I did pretty much everything right. A bit disappointed to come away with second but that's how it goes sometimes. Racing is a pretty cruel business.
"Hopefully that means I get a bit of luck this afternoon in qualifying and tomorrow.
"But, another great start and I had to get my elbows out in that one. Happy with what I did," Piastri said.
Hamilton benefitted from being the first of the frontrunners to switch to slicks and was delighted to be on the podium having won the sprint race in China.
"It's the first time we've been on track in the wet here and what a race it provided us," said the Briton.
"I really, really did struggle on the inters - everyone was struggling on them. I made that call at that end and I said I'm coming in because I was going nowhere. Take the risk, take the gamble and it paid off.
"I wish we had another couple of laps to give these guys a bit of a fight, but big congrats to McLaren."