Hamilton finished third at Mexico City’s Autodromo Hermanos Rodriguez, an eye-watering 0.651 seconds behind Perez, who delighted the exuberant crowd by putting his Red Bull at the top of the order.
The Mexican finished 0.193 sec clear of Verstappen, with Hamilton’s Mercedes team-mate Valtteri Bottas fourth.
The venue for the 18th round of the campaign sits a breathless 2,285 metres above sea level, and the thin air is playing to the strengths of Verstappen’s Red Bull machinery.
While the Dutch driver finished behind Perez in the concluding practice session of the weekend, he will head into qualifying later on Saturday as the strong favourite to secure yet another pole position, and place further pressure on Hamilton.
The Mercedes driver, bidding to win a record-breaking eighth world crown, is already 12 points behind Verstappen in the championship race, and is facing the concerning prospect of seeing his rival pull further into the distance.
When Hamilton’s Peter Bonnington informed him of the large gap to Perez, an almost disbelieving Hamilton replied: “Six-and-a-half tenths?”
Elsewhere, Carlos Sainz finished fifth for Ferrari ahead of AlphaTauri’s Yuki Tsunoda.
Lando Norris, who will start at the back of the grid following an engine penalty, finished 10th.
Qualifying for Sunday’s race gets under way at 2pm local time (8pm UK).
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