Ferrari's Lewis Hamilton was second on the timesheets, 0.345 slower than Norris's impressive lap of 01:16.633 at the Autodromo Hermanos Rodriguez, with Mercedes' George Russell third. Ferrari's Charles Leclerc was fourth fastest.
Piastri, who leads Norris by 14 points, was 0.599 slower than his teammate with Verstappen 0.609 off the pace and complaining about a lack of grip front and rear.
Verstappen, 40 points behind Piastri in the standings but on a charge after three wins in the last four races, had been quickest on Friday while also playing down his long-run prospects.
Mercedes' Kimi Antonelli was seventh quickest with Racing Bulls' Isack Hadjar eighth, Red Bulls' Yuki Tsunoda ninth and Sauber's Gabriel Bortoleto completing the top 10.