Lewis Hamilton claimed his fifth F1 World Title with a fourth place finish enough to clinch the Championship with two races left in the season.
Vettel's display in Mexico was probably his best since the summer break, as he passed both Daniel Ricciardo and Hamilton en route to second place.
It's also Ricciardo's first pole since his victory in Monaco.
"He deserves it. He did the best job this year".
When asked what the difference is now compared to earlier in the year, Verstappen said: "The difference is I just listened to myself and I do my own thing".
"I knew it was in there somewhere", he said moments after roaring over the radio in delight.
The Ferraris looked far more comfortable on the supersoft tyres than their rivals and Vettel pounced to overtake Ricciardo and Hamilton to go second.
In last year's race, Hamilton clashed with Vettel off the line, but the Mercedes driver is eyeing an aggressive start on Sunday. "If there's not, then I'm going to try and hold position", he said.
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Right guard Kyle Long is expected to be out an extended period of time with a right foot injury he sustained against the Jets. The Bills won the last meeting between the teams , 23-20 in overtime in the 2014 season opener at Soldier Field.
Daniel Ricciardo was left feeling "helpless" and keen to hand over his "cursed" Red Bull Formula 1 auto to Pierre Gasly after another mechanical problem robbed him of a podium in Mexico.
Then he snapped at his race engineer Pete Bonnington telling him to leave him to it.
The Australian's rollercoaster year was marred by drama stemming from the relentless engine issues that frayed his relationship with Red Bull and ultimately contributed to his departure for opponent Renault.
"I'm not superstitious or any of that bullsh*t, but the car's cursed".
Lewis Hamilton, meanwhile, looked completely comfortable knowing he's in a ideal spot to win his fifth career Formula One championship.
Hamilton has won four of his five titles with Mercedes and he's contract through 2020, a deal he extended this season.
Quite a drastic turn of fortunes for the two Red Bull drivers.
"It was a shame to lose Daniel. We will get a good tow from the two in front so hopefully I can gain a position".
Mercedes driver Lewis Hamilton, of Britain, drives his vehicle during the Formula One Mexico Grand Prix auto race at the Hermanos Rodriguez racetrack in Mexico City, Sunday, Oct. 28, 2018.
Vettel starts right behind him again Sunday and must win if he has any hope of extending the championship to the next race in Brazil.