Ferrari's Lewis Hamilton, chasing his first pole since Hungary 2023, missed out by a mere 0.012 seconds but was then demoted three places by stewards for impeding Norris's teammate, Australia's Oscar Piastri.
That lifted Ferrari's Charles Leclerc from third to the front row, with Mercedes Formula One leader Kimi Antonelli provisionally taking his place. Piastri moved up a place to fifth.
It was the first time this season, in the 11th round, that Mercedes had not secured pole for a grand prix.
"It was just Lewis not looking in his mirrors," said Piastri, whose engineer Tom Stallard had told him: "I'm sure Hamilton will get a penalty for that."
Piastri added: "A shame, because it meant I didn't get a lap in either way. Clearly the car has been quick today. I've certainly been chasing it, it's not been easy, but clearly there's performance there."
"Very happy to be back on top," said Norris, last year's winner in Hungary who now has a strong chance of repeating the feat at a circuit where overtaking is expected to be tricky with the new era of engines.
"It's been tight the whole weekend but we seemed quick from the first laps we did and we brought a few upgrades. I'm in the best position for the start. But these guys (Ferrari) get good starts and have been fast all season."
Leclerc, who won at Silverstone and was second in Belgium last weekend, will be the immediate threat to Norris, with Mercedes' Antonelli, the championship leader with six wins and 45 points clear of closest rival Hamilton, right behind.
Hamilton, chasing a record-stretching 10th pole at a circuit where he has also won eight times, was fastest after the first runs but was unable to make that stick.
He was then summoned by stewards, with the conversation turning to damage limitation.
"I didn't know he was coming," he said of Piastri. "I thought everyone had finished their lap. It wasn't intentional."
Ferrari team boss Fred Vasseur said it was the team's mistake, with Hamilton not receiving the radio message in time.
Piastri moved up to the second row, with Hamilton on the third row along with Red Bull's four-times world champion Max Verstappen.
Verstappen spun at the end, forcing Antonelli and teammate George Russell to slow.
Stewards also summoned Antonelli for possible speeding while yellow flags were being waved for Verstappen's incident.
"The yellow flag came while I was entering the corner so I tried my best to lift. I did lift but gave up quite a bit of minimum speed compared to before. It was a shame," said the 19-year-old Italian.
Russell qualified seventh for Mercedes, another blow to his chances of closing the gap on Antonelli before the August break, with car gremlins resurfacing after he rode over a kerb and stopped.
"We lost water pressure and I had a water leak. When I stopped on track, the car was leaking a load of water. We don't know where it's come from. Fingers crossed it doesn't affect anything for tomorrow," he said.
Red Bull's Isack Hadjar qualified eighth with rookie Arvid Lindblad ninth for Racing Bulls and Nico Hulkenberg completing the top 10 for Audi. Struggling Aston Martin made a minor breakthrough with Fernando Alonso, four days short of his 45th birthday, making the second phase of qualifying for the first time this season in the team's upgraded chassis.
The Spaniard will start 16th with teammate Lance Stroll 20th but at least ahead of both Cadillacs.
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