Ferrari's Charles Leclerc topped the times ahead of world champion Lando Norris of McLaren in an eventful session that saw Kimi Antonelli wind up fourth as he closes in on the title.
Red Bulls' four-time champion Verstappen was embroiled in an incident that left him with damaged bodywork, tangling with Racing Bulls' Lawson in a feisty fight for track position going into the Foro Sol section.
Verstappen said New Zealand's Lawson caused the trouble near turn 12, their minor collision spewing debris over the circuit and causing the session to be red-flagged for the track to be cleared.
"It was not unlucky," said the Dutchman. "It was not very smart behaviour by him in what he was trying to do there. But it is not going to change my weekend."
Both drivers were summoned by the stewards, who found they behaved in a manner that was "unacceptable" and handed out the penalty.
"I think it is just not very smart behaviour when you are fighting for your seat," Verstappen said, a reference to Lawson's admission this week that he does not know if he will retain his place next season with Racing Bulls, despite an impressive season with the sister team to Red Bull.
Racing Bulls may move to promote Red Bull junior driver Nikola Tsolov, who on Friday became the first Bulgarian driver to take part in an official practice session at a Grand Prix when he drove in FP1.
Lawson has impressed throughout the year and outperformed team-mate rookie Arvid Lindblad comprehensively.
On Thursday he told reporters that finding consistency in formula one is hard, but he believed he has "maximised a lot this year.
"I’m not really sure what more is expected, but I’m not really sitting here thinking too much about the whole seat selection thing.
"I overthought things last year so I’m trying a different mindset this year to score as many points as I can."
Lawson is ninth in the drivers' championship with 77 points while teammate Lindblad is 11th on 38.
His performances have helped lift Racing Bulls to fifth in the constructors' title race behind the big four of Mercedes, Ferrari, Red Bull and McLaren.
He ended up ninth in Friday FP2 while Verstappen was fifth behind the Mercedes of George Russell and 20-year-old Italian Antonelli - who is poised to become the sport’s youngest champion on Sunday if he finishes in the top nine.
Verstappen, a five-time winner in Mexico, admitted: "It could have gone better, but we're not too far off and just have some fine tuning to do. No one has much grip here but it is the same for us all and nothing new."