Norris will start Saturday's (Sunday AEST) 19-lap dash from the front of grid after beating Mercedes' championship leader Kimi Antonelli by 0.222 seconds, with Piastri to start third.
Charles Leclerc will jump from fourth in his Ferrari, while Red Bull's Max Verstappen was fifth fastest and George Russell sixth in the other Mercedes.
The dominant team of last season, McLaren have endured a wretched start to 2026, with Piastri failing to start the first two races before fighting back to finish second in Japan.
At the same time, the Mercedes of Antonelli and Russell have dominated the season's first three races with Ferrari looming as the main challenger.
But after a forced five-week break due to the cancellation of the Bahrain and Saudi Arabia races due to the war in the Middle East, McLaren appear back in the hunt.
The Papaya outfit are one of several teams to have brought extensive updates to Miami, with modifications to front and rear brake ducts, bodywork, the car's floor and rear wing.
Piastri was third quickest in opening practice, before teammate Norris took pole in sprint qualifying after Leclerc had owned the opening stages.
"I'm happy with that," Piastri said.
"The car had good potential, which was really nice to see. We still have things to improve, but the new package is a good step.
"The Ferrari's looked strong throughout the day, so qualifying where we have is a really good effort.
"Whilst we expect the Mercedes to remain competitive, they haven't looked as dominant so far, but there's still a lot of track action to go."
McLaren have won the last two grands prix around Miami's Hard Rock track, with Norris claiming his maiden victory there in 2024 before Piastri's success there last year.
Defending champion Norris is currently fifth in the standings, 47 points behind Antonelli, while Piastri (43) is sixth.
"Perfect way for me to start the weekend," Norris said.
"I've always loved Miami, it's a good result for us. Long way to go but nice to tick it off by doing this.
"This track has always been good to us, we knew the upgrades we were bringing was going to hopefully do a good step and it has."
There are weather concerns around Sunday's race, with forecast heavy rain and thunderstorms which may impact the running.
The FIA is considering various options, in line with Miami state law around the presence of lightning in the vicinity of sporting events, which may include changes to the start time of the 57-lap race.
With PA.
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