In a shrewd tactical move by Red Bull, four-time world champion Verstappen was given an aerodynamic tow behind teammate Yuki Tsunoda, who will start 10th, to lap 0.201 seconds faster than Norris.
He then went 0.088 faster with his second unassisted effort to clock a time of one minute 22.207 seconds, 0.201 faster than championship leader Norris.
Norris moved up from third to second with his second effort after Piastri had looked like qualifying ahead.
Norris chases career-defining podium
The Briton is 12 points clear of Verstappen, and a further four ahead of Piastri, and will be champion if he finishes on the podium in Sunday night's floodlit race at the Yas Marina circuit.
That may not be so straightforward, with Mercedes's George Russell -- fastest in the second phase and in final practice - lurking in fourth place on the grid and Ferrari's Charles Leclerc fifth.
"I am incredibly happy to be in first. That's the only thing we can do, we can control, to maximise what we have and what we can do with the car and we definitely did that in qualifying," said Verstappen.
"Of course I'm excited, I'm looking forward to it. I'm going to try to win that race," added the Dutchman, who will need other drivers' results to go his way.
Norris said he was disappointed not to end the season with a pole but his effort was the best he could do.
"Today, when you look at it we weren't quite quick enough," he said. "I still want to win tomorrow, and that's going to be the goal."
Piastri, who led for much of the season before suffering a devastating drop off, agreed he too had not left a lot on the table.
"It sets up a pretty exciting day tomorrow," said the Australian.
Fernando Alonso qualified sixth for Aston Martin, with Gabriel Bortoleto seventh for Sauber and Esteban Ocon eighth for Haas.
Verstappen's future Red Bull teammate, Isack Hadjar, will line up ninth for Racing Bulls with Tsunoda alongside.
Russell's teammate, Kimi Antonelli, is likely to be less of a factor in Sunday's proceedings after qualifying 14th.
Ferrari's Lewis Hamilton completed a miserable hat-trick by failing to get through the first qualifying phase for the third race in a row.
The seven-time world champion, who joined Ferrari from Mercedes in January amid a wave of optimism, will start 16th in his last chance to avoid a season without a podium finish for the first time.
Hamilton qualified 18th in Qatar a week ago and last in Las Vegas.
Alpine's Pierre Gasly and Franco Colapinto qualified last for the team's final race with Renault power before switching to Mercedes next year.
