Norris ended his six-race run without a pole, his last coming in Belgium in July, by dominating the field and beating Ferrari's Charles Leclerc by 0.262 seconds.
It was a significant boost to his title hopes as rivals Max Verstappen and Piastri struggled to fifth and eighth respectively.
Piastri will start seventh due to a grid penalty for Williams' Carlos Sainz but the Australian has been well off the pace all weekend and was almost six tenths adrift.
Lewis Hamilton claimed third on another impressive day for Ferrari and he will be hopeful of landing his first podium for the Scuderia on Sunday.
Norris said he was happy to be finally back at the front of the grid.
"It's actually been quite a long time so it's a good feeling," he said.
"I've had some good races here in the past, so I just focus on what I can control and that's what I can do.
"It was an incredible lap. There were a couple of places where I thought I messed up a touch.
"When I saw a 15.5 there was a big smile on my face. It was one of those laps where it all came together.
"It is not often this year I get that feeling in this car, despite how good it is."
Piastri described qualifying as a "frustrating session" and said his speed was just off.
"Everything felt pretty normal, the lap times just haven't been there," he said.
"There's just no pace which is a bit of a mystery. It's just this weekend and last weekend it's felt like the pace hasn't come.
"I'll try my best (in the long run to turn one). That's going to be an opportunity to make some progress forwards. We'll see what I can do."
Verstappen arrived in Mexico City as the man in form, having roared back into championship contention by winning three of the last four races, and was favourite to rack up another victory in Mexico City - where he has won five times before.
He trails Piastri by 40 points - down from 104 five races ago - and is 26 behind second-placed Norris with 141 points still to fight for.
The Autodromo Hermanos Rodriguez boasts the longest run from pole to the turn one braking point on the F1 calendar, and Norris will be braced for a testing 830m dash when the lights go out on Sunday.
The Mexico City circuit is also one of the trickiest with the low air density at altitude making it difficult to generate downforce.
Verstappen was one of the drivers struggling for balance in the opening session of qualifying and was only ninth-fastest, with Racing Bulls' Isack Hadjar leading the way and Norris fourth.
Piastri narrowly squeezed through the third qualifying session by less than a tenth, with relief etched on the face of team principal Andrea Stella, but was no threat to pole and has major work to do on Sunday to prevent significant damage to his title lead.
Leclerc surged to provisional pole in the first runs in the final session but Norris found the answer with his run, a scintillating 1.15.586 second lap which could prove pivotal in his title bid.
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