Hamilton also faces an investigation for failing to slow sufficiently for the yellow flags waved when Leclerc lost control.
Norris topped all 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 difficult, 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.”
Rain is forecast for Saturday morning in Sao Paulo, when the sprint race is due to start at 14:00 GMT. Qualifying for the grand prix is at 18:00.
Piastri, who comes to Brazil after two difficult races in the US and Mexico, said: “The soft [tyres mandated in the final session] was a bit different to what I expected, 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.”
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 and 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.”
