George Russell will line up third for Mercedes and Ferrari's Charles Leclerc and Carlos Sainz fourth and fifth with an upgraded car.
Red Bull's Formula One championship leader Max Verstappen qualified seventh, one place behind Mercedes' seven-time world champion Lewis Hamilton.
Verstappen leads Norris by 70 points with nine races remaining but the Briton could take a chunk out of that on Sunday.
"Another pole which is amazing," said Norris, who qualified fastest also in the Netherlands last Saturday before winning on Sunday.
His pole time of one minute 19.327 seconds, on a sunny afternoon in the former royal park near Milan, was 0.109 quicker than Piastri's best effort with Russell 0.113 off the pace and Leclerc 0.134.
"To have two cars, first and second, when the field has been as tight as it has been this weekend, is surprising," added Norris, who is now targeting his third career win.
"It hurts me to say it, but my lap was not a great lap. However, it was still good enough for pole, so I was surprised, but happy."
Flying Lap
Norris was fastest in the first phase of qualifying and secured provisional pole in the top 10 shootout before improving on it with his second flying lap.
Hamilton had been top in the second phase with Verstappen second and Norris third.
Sunday's race at the 'Temple of Speed' near Milan could be a tight battle between the top four teams.
McLaren are only 30 points behind champions and leaders Red Bull and could make significant inroads in that constructors' battle.
Red Bull team boss Christian Horner said the once-dominant car's balance was off and suffering a lack of grip on a completely resurfaced track, with Verstappen 0.695 off Norris's pole time
"We need to address it quickly as McLaren have made a significant step over the last few races and we are now behind Ferrari and Mercedes as well," Horner told Sky Sports television.
"Something is clearly not working on the car. There will be an engineering solution to an engineering problem."
Hamilton was also unhappy, chiding himself for a missed opportunity at a circuit where he has won a record-equalling five times.
"I am furious, absolutely furious. I could have been on pole, at least on the front row. I just didn't do the job," said the Ferrari-bound Briton.
"I lost a tenth and a half into Turn One, and then a tenth in the last corner. No one to blame but myself."
Mexican Sergio Perez qualified eighth for Red Bull with Alex Albon ninth for Williams and Nico Hulkenberg completing the top 10 for Haas.
Formula One's Argentine newcomer Franco Colapinto, replacing Logan Sargeant at Williams, qualified 18th and ahead of both Saubers.
