Lewis Hamilton claimed a crucial win in his bid to clinch the Formula One championship with a magnificent performance at the Sao Paulo Grand Prix.
Verstappen had extended his lead in the title race on Saturday when he finished second behind Hamilton's Mercedes team-mate Valtteri Bottas in the sprint qualifying race.
Hamilton had his Friday qualifying session result ruled out due to a DRS infringement, meaning he started the sprint race in last, but went from 20th to fifth, only for a five-place grid penalty to mean he started 10th on Sunday.
Yet the reigning world champion delivered a memorable win, gaining eight places within the early exchanges before, at the third attempt, he overtook Verstappen with 12 laps remaining.
Verstappen and Sergio Perez had nipped ahead to make it a Red Bull one-two early on, with Bottas unable to keep control of the race, but Hamilton ensured it was Mercedes' weekend.
The safety car was deployed early on, with Yuki Tsunoda and Lance Stroll colliding, while Lando Norris sustained a puncture on the first lap and was forced to pit immediately.
Hamilton had made a brilliant start, however, and his charge up the track saw him catch leader Verstappen on the 48th lap.
Verstappen did not open up space at turn four, forcing Hamilton wide, with both cars going off the track before straightening up with the Red Bull retaining its lead.
To Mercedes' frustration, the incident was noted by stewards, but not investigated. Hamilton tried again 10 laps later, yet again found his path blocked by Verstappen, who weaved on the straight.
It only delayed the inevitable, however, as Hamilton made it third time lucky when he finally got beyond his title rival ahead of turn four on lap 59.
Verstappen's frustration was compounded by a penalty for his weaving a lap previous, though Perez did at least collect the fastest lap to take a point away from Hamilton, with Bottas rounding off the podium.
DID VERSTAPPEN GET LUCKY?
It was an almighty tussle between the title rivals on turn four at lap 48, with Verstappen just managing to hold onto his advantage.
Hamilton, who labeled the incident "crazy", was sure there had been an infringement, but with it unclear as to whether Verstappen had driven his counterpart off the track, the FIA decided not to investigate, much to Mercedes' chagrin.
HISTORY FOR HAMILTON
Hamilton has now won 17 races in the Americas (seven in Canada, six in the United States, two in Brazil and two in Mexico).
It means he overtakes the legendary Michael Schumacher as the driver with the most F1 victories across the four nations.