The usually hour-long session was stretched over 85 minutes by intermittent rain and two red flags, including for the under-pressure Sergio Pérez at Red Bull Racing and Yuki Tsunoda at RB.
Norris kept a cool head throughout to build into a dominant position in the pole shootout, in which he set just one lap that proved quick enough to take top spot.
The Briton set the benchmark at 1 minute 15.227 seconds, pipping teammate Piastri by just 0.022 seconds.
There would likely have been more on the table too were it not for Tsunoda’s late smash, coming with just over two minutes left on the clock.
The Japanese driver ran wide exiting turn 5, where the kerbs and astroturf launched his RB car into the barrier, where it copped massive damage and forced a red flag.
There was just enough time to resume the session, but almost no driver could improve on their quickest laps on used tyres, securing Norris top spot.
“Very, very happy,” he said. “It wasn’t an easy qualifying - different conditions - but always ending up on top.
“I’m happy especially for the team. A one-two is even better to see, so congrats to the team.”
Piastri lamented the narrow margin to what would have been his maiden pole position but celebrated the team cementing its first front-row lockout since the 2012 Brazilian Grand Prix.
“I’m very happy,” he said. “Of course when you miss out by 0.02 seconds you think of what you could do a little bit better, but an amazing result for the team.”
Verstappen qualified 0.046 seconds behind pole-getter Norris but was frustrated Red Bull Racing’s upgrades this weekend had come up short.
“The whole weekend I think we’ve been a little bit behind, and I think that was also the case in qualifying,” he said. “I tried to make it as close as possible, but unfortunately just not enough.
“It’s a bit difficult pinpoint why that is. I would’ve liked a bit more grip, but it’s not there at the moment.”
Carlos Sainz qualified fourth but was a distant 0.469 seconds off pole in the quickest Ferrari.
Mercedes’s Lewis Hamilton will line up fifth alongside Charles Leclerc in the second Ferrari at more than 0.6 seconds off the pace.
Aston Martin teammates Fernando Alonso and Lance Stroll qualified seventh and eighth respectively ahead of Daniel Ricciardo and RB teammate Tsunoda in ninth and 10th.
Nico Hülkenberg qualified 11th for Haas ahead of Sauber’s Valtteri Bottas and Williams teammates Alex Albon and Logan Sargeant, with Kevin Magnussen putting the second Haas car 15th in the order.
The under-pressure Pérez crashed out of qualifying just over 11 minutes into the session, turning up the blowtorch on his future with Red Bull Racing.
Pérez lost control of his car at turn 8 when he mounted the damp kerb on entry. His RB20 immediately snapped from under him and catapulted itself into the far barrier, smashing into the barrier.
Pérez has been under pressure to improve is form under threat of losing his seat after August’s midseason break, but slumping to 16th on the grid in his fourth Q1 elimination in the last six grands prix will have done nothing to help his case.
The 10-minute red flag that ensured to clear his wrecked car coincided with a brief shower that reset the track, and the Q1 order was subsequently decided by who timed their laps best to capitalise on the drying conditions.
George Russell got it badly wrong as one of the first on track and without having taken enough fuel to make it to the end of the session. He was eliminated 17th ahead of Zhou Guanyu.
Alpine was the only team to manage the final frenetic minutes of Q1 worse than Mercedes, electing not to send Esteban Ocon and Pierre Gasly to the track at all, leaving them the tumble helplessly down the order to 19th and 20th.