Piastri leads Norris in McLaren practice one-two ahead of qualifying in Mexico City
The Australian, who could be mathematically out of the title chase after Sunday's race at the Autodromo Hermanos Rodriguez, lapped with a best time of one minute 16.492 seconds with Norris 0.059 slower.
Ferrari's Carlos Sainz was third, 0.340 off the pace, and Red Bull's championship leader Max Verstappen was fourth and 0.511 slower than Piastri.
Verstappen, who leads Norris by 57 points with five rounds remaining, had a difficult Friday but Red Bull swapped out his engine overnight and replaced it with a previously used one, avoiding any penalty.
The triple champion complained of a lack of grip, however.
Teammate Sergio Perez, the local hero but enduring a terrible run of form, was only 14th after also struggling on Friday.
Seven-times world champion Lewis Hamilton was fifth for Mercedes, with Ferrari's Charles Leclerc sixth on the timesheets.
Mercedes' George Russell, who crashed heavily on Friday, returned with a rebuilt car after mechanics worked late and broke curfew for the second time this season but without penalty. He was eighth.
Mercedes said the chassis had been changed but the power unit and gearbox were OK.