In only the second championship chase to see the top two enter the final race of the season all square on points, Verstappen had to match Hamilton but struggled to do so for much of Sunday's remarkable race.
Red Bull was furious following an early flashpoint that had Hamilton ahead, yet Mercedes were outraged by the chequered flag as Verstappen, on fresh tyres, was allowed a single lap after a safety car to take the title.
Hamilton looked to have done everything right but paid for Mercedes' call not to bring him into the pit lane in the closing stages.
A tough start had been forecast for Hamilton when he stuck with medium tyres while Verstappen – and others close behind – used softs. Instead, rapid reactions at lights out put the Mercedes in front.
But then the drama truly began, as Verstappen looked to go up the inside at Turn 7 and Hamilton was forced wide and off the track to avoid contact.
The defending champion clearly gained an advantage and pulled away from his rival, only for the stewards – in a decision Verstappen considered "incredible" – to deem Hamilton had given enough time back.
Verstappen and Hamilton both switched to hards in the pits, putting the frontrunner behind Sergio Perez in the second Red Bull car.
Perez doggedly held Hamilton up and brought Verstappen back into play before the Silver Arrow finally got through, able to again build a big lead until a virtual safety car provided another twist.
With Hamilton staying out, Verstappen headed in for a cheap pit stop, potentially setting up a nervy finish with a 17-second deficit on fresh tyres.
Verstappen struggled to find the requisite pace but was given another lifeline by a safety car with four laps remaining.
Again he pitted as Hamilton did not and a dramatic finish saw lapped cars allowed to pass the safety car, infuriating Mercedes and leaving Verstappen one lap to go at the race leader, who he decisively passed at the last.
'NO, MICHAEL, NO!'
This was a day to tune into the team radios, with a number of intriguing exchanges as momentum swung back and forth.
Verstappen hailed Perez as a "legend" for delaying Hamilton, while the Mercedes man considered his team's decision not to box "a bit of a risk" long before another gamble spectacularly backfired.
But Toto Wolff's pleas to race director Michael Masi were the obvious standout, as Hamilton was left exposed on the final lap. "We went car racing," replied Masi.
MAX MAKES HIS MARK
Hamilton fell just short of history on this occasion, stuck on seven titles alongside Michael Schumacher, but there was a new landmark for champion Verstappen.
His 18th podium of the year was undoubtedly the sweetest and made the Dutchman the first man to reach that mark in a single F1® season.
RAIKKONEN RETIRES IN PITS
Away from the title race, Kimi Raikkonen's record-extending 351st and final grand prix in Formula 1® did not end as planned, with the veteran experiencing braking issues and hitting the barriers at Turn 6 as his rear axle locked up.
Although Raikkonen's Alfa Romeo limped back to the pits, he could not continue and was given a standing ovation as he prematurely exited his car.
1. Max Verstappen (Red Bull)
2. Lewis Hamilton (Mercedes) +2.256s
3. Carlos Sainz (Ferrari) +5.173s
4. Yuki Tsunoda (AlphaTauri) +5.692s
5. Pierre Gasly (AlphaTauri) +6.531s
6. Valtteri Bottas (Mercedes) +7.463s
7. Lando Norris (McLaren) +59.200s
8. Fernando Alonso (Alpine) +61.708s
9. Esteban Ocon (Alpine) +64.026s
10. Charles Leclerc (Ferrari) +66.057s
1. Max Verstappen (Red Bull) 395.5
2. Lewis Hamilton (Mercedes) 387.5
3. Valtteri Bottas (Mercedes) 226
4. Sergio Perez (Red Bull) 190
5. Carlos Sainz (Ferrari) 164.5
1. Mercedes 613.5
2. Red Bull 585.5
3. Ferrari 323.5
4. McLaren 275
5. Alpine 15