The 20-year-old Red Bull driver lapped the Autodromo Hermanos Rodriguez with a fastest lap of one minute 17.113 seconds, a track record.
Hamilton, who has a 66-point lead over Ferrari's Sebastian Vettel and need only finish fifth on Sunday to become Britain's first four-times world champion, was 0.075 slower on a sunny morning in the capital.
The Mercedes driver was second fastest in both of Friday's sessions, with Verstappen's team mate Daniel Ricciardo setting the pace in the afternoon.
Vettel was third fastest on Saturday, 0.117 off Verstappen's pace and setting up the prospect of a tight battle for pole position in later qualifying.
Mercedes, Red Bull and Ferrari filled the next three slots with Valtteri Bottas, Daniel Ricciardo and Kimi Raikkonen.
Home hero Sergio Perez was seventh, ahead of Force India team mate Esteban Ocon.
New Zealander Brendon Hartley was an impressive 11th fastest on only his second race weekend for Toro Rosso.
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
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