Mercedes' Kimi Antonelli joined the Briton - who won last year's sprint - on the front row for Saturday's race at Interlagos.
Norris is a point clear of Piastri in the overall standings with four grands prix and two sprints, including Saturday, to come. The 100km race offers eight points to the winner, with the top eight scoring.
The sprint race offers eight points to the winner, with the top eight scoring.
Rain expected for Saturday's race
"We did the job we needed to do, which was to be fastest today," said Norris, who took the lead from Piastri in Mexico last month.
"Trickier than Mexico. I’ve not been feeling quite as comfortable, but therefore it’s a great result.
"It’s meant to rain a lot in the morning, it’s meant to be incredibly windy, so make sure everyone brings their rain jackets," he added.
Piastri's third place on the grid left the Australian looking more competitive and happier than he has sounded of late.
"We can definitely fight with what we’ve got, and there’s obviously a lot more points on Sunday," said the Australian.
George Russell will line up fourth for Mercedes, at a track where he took his first win in 2022, with Aston Martin's Fernando Alonso fifth after setting the fastest time in the second phase.
Four-times world champion Max Verstappen qualified an unhappy sixth.
"The car is completely broken, it's just undrivable," said the Dutch driver, last year's grand prix winner from 17th on the grid but now 36 points behind Norris, over the radio after the second of the three phases.
Team boss Laurent Mekies sympathised: "Honestly, he's very unhappy with what the car does at the moment, so that's what you heard on the radio," he told Sky Sports television.
"When you cannot push the car to the limit the way you like, that's the sort of feedback you get. That's fair enough."
Ferrari's Lewis Hamilton failed to reach the final top-10 shootout, qualifying 11th after running out of time to cross the line for a final flying lap in phase two (SQ2) and was called to the stewards afterwards for failing to slow for yellow flags.
"Yeah, every time mate," said the unhappy seven-times world champion over the radio after being told by race engineer Riccardo Adami that he was P11.
Teammate Charles Leclerc made it through, despite spinning at the end of that phase and triggering the double yellow flags that denied others the chance to go faster. He qualified eighth, behind Aston Martin's Lance Stroll.
Racing Bulls' Isack Hadjar will line up ninth and Sauber's Nico Hulkenberg completed the top 10.