Lewis Hamilton was knocked out in the second session and qualified 11th in his Ferrari, his final lap in the second session ruined when team-mate Charles Leclerc spun in front of him out of Turn 10.
Hamilton also faced an investigation for failing to slow sufficiently for the yellow flags waved when Leclerc lost control but was let off with a reprimand, because of the short time a yellow signal was visible to him and the fact he had hesitated before applying the throttle.
Norris’ result is the best possible start to the weekend and gives him the opportunity to build his championship lead – eight points are awarded to the winner of the sprint, seven for second and so on down to eighth place.
Norris topped two of the three sessions in sprint qualifying and had a comfortable advantage over Piastri throughout.
He said: “It was a little bit tougher than I would have liked. But we did the job we needed to do, which was to be fastest today.
“Qualifying is always one of the best things here. It’s difficulty, it’s bumpy, it’s tricky, always a joy, always puts a smile on your face.
“But a long weekend, another qualifying and another couple of races to go but a good start.”
Piastri, who comes to Brazil off the back of two difficult races in the US and Mexico, said: “A couple of big moments on my first lap, which wasn’t ideal.
“That was a shame. But ultimately I felt much happier than the last couple of weeks. We can definitely fight with what we’ve got and there are a lot more points on Sunday.”
Qualifying for the grand prix is due to follow the sprint at 18:00 GMT, although the weather forecast means the schedule could well be affected.
Verstappen complained over the radio to the team that his car was “undriveable”.
He added: “A lot of vibration in the car, a lot of ride problems. Not what we want. But besides that we also don’t have the grip, just can’t get the car to turn but at the same time can’t really rely on the rear.
“For us, quite poor, I would say. It is quite clear we are lacking something. I am not expecting that to be much better in the wet. But we’ll see tomorrow.”
