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 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.”
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.
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.
Antonelli impressed in second, his best time set on his first lap, while the surprise package of qualifying was Alonso, who set the fastest time in the second session and was just 0.253secs off pole in his midfield car in the final shootout.
His team-mate Lance Stroll was seventh fastest, ahead of Leclerc, Racing Bulls’ Iscak Hadjar and Sauber’s Nico Hulkenberg.