Hamilton had to overcome first-lap chaos when his Mercedes was bumped by title rival Sebastian Vettel of Ferrari. Hamilton got a tire puncture and Vettel had wing damage. Both had to stop immediately for repairs.
That left them in a furious bid to catch up as Verstappen sped away to victory. Vettel finished fourth but had to win or finish second to push the title chase to the last two races in Brazil and Abu Dhabi.
Hamilton's championship makes him the most decorated British driver in F1 history, passing Sir Jackie Stewart. He is one of only five drivers in F1 history with four or more.
Hamilton held his helmet in his hands as he crossed the finish line, then took a lap around the track while waving the British Union Jack.
Vettel didn't make any of it easy, in more ways than one.
A wild start saw Verstappen bump the Ferrari while fighting through the first turn at the end of the track's long straight. Verstappen got the edge and got out when Hamilton made a move to get past Vettel, who drifted left. The Ferrari's left front wing clipped Hamilton's right rear tire, damaging both cars and forcing their drivers to pit for repairs.
As Verstappen pulled away, a seething Hamilton asked his team over the radio if Vettel made contact "on purpose."
"Not sure, Lewis," the team replied. Race stewards determined no investigation was necessary.
Both drivers made a mad scramble to get back toward the front, weaving through the traffic that bottles up a short track at the Autodromo Hermanas Rodriguez, and Hamilton was struggling to make up any ground. On lap 23, he was so slow that he was shown a blue flag, the order to let a faster car - Verstappen - go past him.
Vettel was on a furious pace to push the championship to the next race. He never got close. Late in the race, he asked his team if he could get second but when told how far behind he was, Vettel replied, "Oh mama mia, that's too much."
The finish allowed Hamilton to celebrate championships in four cities, with Mexica City joining Sao Paolo, Brazil, in 2008, Abu Dhabi in 2014 and Austin, Texas, in 2015.
"Viva Mexico!" Hamilton told the crowd when he got out of his car.
Hamilton's championship will spur questions about his place among the best drivers in F1 history. The 32-year-old joined Vettel and Alain Prost as four-time winners. He now trails only Argentina's Juan Manuel Fangio (five) and Germany's Michael Schumacher (seven) for the most of all time.
He surpassed the three won by his idol, Brazilian Aryton Senna, who is still considered one of the most elegant and skillful drivers in F1 history.
Hamilton's Mercedes car has dominated the era of turbo-hybrid engines adopted in 2014. Of Hamilton's 62 career victories, 30 have come over the last four years, a span of 77 races.
He chased down this championship over the second half of the season after Vettel won two of the first three races. Ferrari faltered as Hamilton had racked up five wins over the past seven races and his car has been as steady as his driving. Hamilton has finished every race and missed the podium just five times....