A day after his Red Bull team were fined £6million for breaching Formula One's financial rules last year, Verstappen delivered a breathless lap in the thin Mexico City air to take the qualifying spoils.
George Russell finished second, 0.304 seconds behind Verstappen, with Hamilton 0.309secs further back.
Hamilton finished runner-up to Verstappen at last weekend's United States Grand Prix before promptly ruling out any hope of ending the campaign with a victory ahead of the final three rounds.
However, just six days later, Hamilton, armed with a new front wing on his Mercedes, had a machine capable of taking the fight to Verstappen and Red Bull.
Hamilton's first lap in Q3 was deleted for exceeding track limits at Turn 3. He then complained about the lack of speed from his machinery.
"I have got drivability issues," he reported to his race engineer, Peter Bonnington over the radio. "Power dropping out."
Hamilton returned to the track for his final run, and was just 0.014secs adrift of Verstappen after the second sector.
But the seven-time world champion was unable to carry his pace through the final third of the lap, finishing a distant three tenths back.
"We had some problems with the engine towards the end, and there was definitely a bit of performance left on the table," said Hamilton.
"The problem started to appear in Q2, and then after that, every run in Q3. I was dropping out of power on the exit of corners. It felt like an ignition issue but I will find out more from the team.
"I did the best I could and losing that first lap made the last one very difficult. I had to be very reserved to make sure it was clean and I wasn't as able to push as hard as I would have liked.
"But nonetheless, it is not a bad position to start from and I hope we can fix the engine problem."
The 811-metre charge to the first corner resembles the longest on the F1 calendar, and Hamilton is hopeful he will be able to take advantage of a tow off Verstappen's Red Bull at a track which sits 2250 metres above sea level.
Hamilton might also be encouraged that the last two races at the Autodromo Hermanos Rodriguez have been won from third on the grid.
But the British driver warned: "These guys (Red Bull) have been rapid all year long, and we are still losing out to them through straight-line speed.
"It will be difficult to get by, but we will give it our best shot and Turn 1 is an opportunity. We will go for it."
Hamilton's team-mate Russell, fastest in both second and third practice, was also in a position to challenge for pole.
But he ran wide through the stadium section, scuppering his hopes of claiming both his and Mercedes' second top spot in qualifying of the year.
"Sorry guys," said a deflated Russell over the radio.
He added afterwards: "The team deserved more today. They've produced a really great car. I feel like it was our pole to have, but it was just a terrible lap from my side."
Verstappen has already sewn up his second title but he will surpass Michael Schumacher and Sebastian Vettel and claim the record of most victories in a single campaign if he triumphs for a 14th time in 2022 on Sunday.
The home crowd, however, will be desperate to see the other Red Bull triumph, with 350,000 spectators in Mexico's capital this weekend to cheer on Sergio Perez at the 20th round of 22. Perez will start from fourth on the grid.
P3 start tomorrow! So so proud of my team, they’ve been on it all weekend and this is best qualifying we’ve had all year. Heads down for tomorrow, it’ll be hard work for sure but we’re excited for the fight ðð&34;ð¥ pic.twitter.com/akaGzmPEmy— Lewis Hamilton (@LewisHamilton) October 29, 2022