Forty-eight hours after Red Bull were fined £6million for breaking the sport's financial rules - before the team went on to boycott Sky Sports' coverage - Verstappen claimed his 14th win of the year.
Michael Schumacher won 13 of the 18 races staged in 2004. Sebastian Vettel recorded the same number of wins from 19 rounds in 2013. But Verstappen now stands alone as the driver with the most wins in a single campaign.
Lewis Hamilton hoped a different tyre strategy to Verstappen would propel him to his first win of the year.
But he crossed the line 15.1 seconds behind Verstappen, with Sergio Perez third. George Russell finished fourth for Mercedes.
Verstappen said: "The start helped me out a lot to stay in the lead. We were on a different strategy but an incredible result.
"It has been an incredible year so far. We are enjoying it and we will try to go for more wins."
The 811-metre charge to the opening right-left-right chicane at the Autodromo Hermanos Rodriguez is the longest on the calendar.
Hamilton, starting in third - the grid slot for the past two winners at this venue - said it would resemble his best shot of knocking Verstappen off his perch.
But Verstappen won the drag contest at a canter, keeping both silver machines in his mirror as he navigated the opening three bends unopposed.
Instead, the drama unfolded behind the double world champion with Hamilton moving ahead of Russell at the third corner.
Hamilton's no-nonsense move on Russell saw his junior team-mate run wide over the kerbs, allowing Perez to carry the momentum on the run down to Turn 4 and usurp Russell. Cue wild celebrations in the Mexican stands.
Verstappen raced around the first lap to build up a 1.3 second lead. Hamilton, on the durable, but slower medium tyre compound was keeping his rival on his toes.
Perez, like team-mate Verstappen, started on the speedier soft rubber, and he was the first to stop on lap 23. But Perez was stationary for five seconds as Red Bull struggled to bolt on his rear-left tyre.
Two laps later, and it was the turn of Verstappen, 1.5secs ahead of Hamilton, to dive into the pits for the medium tyres. There were no dramas for the Dutchman as he rejoined in third, with Hamilton heading Russell in a Mercedes one-two.
How long could the Mercedes pair travel on their medium rubber? The answer arrived on lap 29 of 71 when Hamilton stopped. Russell lasted another six laps.
Both Mercedes drivers were now on the hardest rubber, hopeful, not only of getting to the end, but that Verstappen, on the medium tyre, would not.
A chess match followed. Hamilton and Russell were complaining about the speed of the hard rubber, but were matching the lap times of both the Red Bulls. Could it have been a coded message to their rivals?
Yet, as the lap counter ticked down, and Verstappen showed no sign of stopping, alarm bells started ringing inside Hamilton's helmet.
"Are we on the wrong tyre, mate?" he asked. "No, Lewis, we think we are on the right tyre," replied his race engineer Peter Bonnington. "We are going to get to the end of this no sweat?"
However, the rub for Mercedes was that Red Bull looked set to make it over the line, too.
Hamilton was back on the radio.
"This medium looks quick, mate," he said. "They are going to go the end." Perhaps tellingly, Bonnington did not reply.
Hamilton's fears came true, with Verstappen cruising to the chequered flag and making history.
Speaking after the race, Hamilton, who was jeered by the partisan Red Bull fans, said: "This has been an amazing crowd, a bit awkward this time round, boos all day, but nevertheless I have so much love for Mexico and the people here.
"I was close in that first stint, but the Red Bulls are too fast, and ultimately they had the better strategy. I am not sure it was the right tyre. I thought we should have started on the softs."
On an afternoon of rare incident in the high-altitude Mexico City air, Daniel Ricciardo clashed with Yuki Tsunoda. "What the f*** is he doing," said Tsunoda who had to retire with the damage sustained.
Fernando Alonso parked his Alpine after his engine conked out with six laps to go. The Virtual Safety Car was deployed but had no impact on the result.
Carlos Sainz finished fifth for Ferrari, one place ahead of team-mate Charles Leclerc with Ricciardo seventh.