Piastri, Norris set Mexico practice pace as Verstappen struggles
Piastri clocked a best lap in one minute and 16.492 seconds to outpace the title-chasing Norris by 0.059 ahead of Ferrari's Carlos Sainz.
Three-time world champion and series leader Max Verstappen, who leads Norris by 57 points with five of this year's 24 races remaining, was fourth for Red Bull, ahead of seven-time champion Lewis Hamilton of Mercedes and Charles Leclerc in the second Ferrari.
Yuki Tsunoda was seventh for RB ahead of George Russell, in the second Mercedes, Kevin Magnussen of Haas and Liam Lawson of RB.
McLaren's strong showing was a perfect riposte after the stewards had rejected their application for a right of appeal following Norris's five-second penalty at the United States Grand Prix last Sunday.
On a bright morning, with a track temperature of 33 degrees and the air at 17, Russell was first out for an installation lap checking his car following an overnight rebuild.
After his high-speed crash on Friday, it was proof too of the driver's strength of mind.
Verstappen was also out early to test his power unit, changed overnight after problems on Friday, and he soon swept to the top of the times only to be beaten by Russell.
As the session settled down, in front of a noisy crowd, Hamilton took control in 1:18.123 after 17 minutes only for Ferrari to respond with Sainz going three-tenths quicker ahead of Leclerc.
Sainz's improved lap in 1:17.334 kept him on top before a brief drama when RB's Liam Lawson spun off a kerb in the stadium section. He extricated himself without incident.
After running on mediums, most of the field switched to softs with 15 minutes remaining.
Almost immediately, Verstappen took the initiative with a lap in 1:17.003 before the McLarens took over with Norris and then Piastri going fastest in succession.
It was clear that, despite their disappointment in failing to gain a right of review of Norris's five-second penalty in Texas, McLaren were focused and fast while Verstappen was grumbling about lack of grip "front and rear".