Verstappen moves ahead of Michael Schumacher and Sebastian Vettel for number of races won in a season
The world champion held off a challenge from Lewis Hamilton's Mercedes in the first part of the race before pulling away to take his 14th win of the year.
It moves the Dutchman clear of Michael Schumacher and Sebastian Vettel, who won 13 races in 2004 and 2013.
Red Bull's Sergio Perez took third ahead of Mercedes' George Russell.
Mercedes had hopes of winning the race after qualifying close behind Verstappen in second and third places.
But, on divergent tyre strategies, early promise faded after the pit stops and Verstappen moved into a race of his own, leaving Hamilton to fend off Perez for runners-up spot.
Red Bull started on the 'soft' tyre and Mercedes on the 'medium', and the question was how the different strategies would play out.
Verstappen managed to hold the lead into the first corner - only the second time that has happened for the pole man in five races in Mexico - while Hamilton snuck past Russell into second at the second turn, followed by Perez two corners later.
Hamilton tracked Verstappen closely in the first stint, and it was clear Red Bull were feeling the pressure from the Mercedes.
But the tension dissipated shortly after Red Bull stopped for tyres on lap 25, fitting the mediums, followed by Hamilton four laps later, fitting the hards.
Hamilton was now set to go to the end without another stop, and the question was whether Verstappen could do the same.
It soon became apparent that the hard was not a good tyre, as Hamilton, who emerged 6.5 seconds behind Verstappen, began slowly to drop away from the Red Bull.
Hamilton repeatedly complained about his tyres lacking performance, and was reassured by his engineers that the mediums would drop away towards the end of the race.
But they hung on just fine, and Verstappen took another untroubled win.
"In hindsight, maybe not the right tyre choice," Mercedes team boss Toto Wolff said over the radio to Hamilton on the slowing down lap.
Hamilton said in the post-race interviews that he thought Mercedes should, like Red Bull, have started on the soft.
The leaders' pit stops promoted Russell into the lead, and he asked his engineers to leave him out and change to the soft tyres for a sprint later in the race.
But the engineers decided that was not a good plan and they brought Russell in for his stop five laps after Hamilton, resuming in fourth place, where he stayed to the end.
There will inevitably be questions as to whether Mercedes would have been better off to follow Russell's suggestion.
It would have meant making up a lot of ground and leaving him three cars to overtake for the win, but in the worst case scenario he would have been no worse than fourth, and there was potential gain in taking the risk.
This was demonstrated by Daniel Ricciardo, who did go for the medium-soft strategy, and made up a lot of ground in doing so, moving up from out of the top 10 to finish seventh, and best of the midfield behind the two uncompetitive Ferraris of Carlos Sainz and Charles Leclerc.
It was almost certainly Ricciardo's best drive of a year that has been so disappointing that McLaren terminated his contract a year early.
It was as if the swashbuckling Ricciardo of old had returned. But he now has only two races remaining before an enforced sabbatical, in which he may be a reserve driver for either Mercedes or his former team Red Bull - he is in talks with both teams, Wolff said on Saturday.
The Australian was given a 10-second penalty for colliding with Yuki Tsunoda's Alpha Tauri and forcing it into retirement, but such was his pace that he kept seventh place because his gap to Esteban Ocon's Alpine behind was more than that.
Ricciardo was helped in moving up by yet another technical problem for Fernando Alonso's Alpine.
The Spaniard led the midfield in seventh place most of the race but began to drop back in the closing stages as his engine developed a problem and it eventually failed with six laps to go.
Alonso's problem promoted Ocon to eighth, ahead of McLaren's Lando Norris and Alfa Romeo's Valtteri Bottas who just held off the charging Alpha Tauri of Pierre Gasly - another to go for the medium-soft strategy - on the final lap.
-- Courtesy of BBC Sport