Owing to crashes and debris, the first half of the race was stop-start, but the closing stages will go down in Formula 1 history, Hamilton colliding with his rival before finishing 11 seconds clear after Verstappen had been hit with a five-second penalty.
Adding the point for his fastest lap of the race, Hamilton moves level on points with Verstappen ahead of the final race of the season in Abu Dhabi.
Mercedes made the perfect start, retaining first and second respectively, and everything appeared to be going to plan ahead of Hamilton making his first stop.
However, a heavy crash, not for the first time on Sunday, halted proceedings, not only handing Verstappen a way back into the race but a clear advantage having already pitted and with Hamilton having not.
For the drivers as well as observers, the race became difficult to assess as it became dominated by red flags, safety cars and lingering debris, but Verstappen led with 15 laps left.
Moments after Verstappen had aggressively retained his advantage, the pair, already holding a rivalry full of controversy, then collided, Hamilton going into the back of the frontrunner and claiming that he had "brake-tested" him.
After a bizarre set of circumstances, Verstappen was ordered to give Hamilton first position, only to immediately overtake his rival, a move that even his team disagreed with.
Verstappen was ultimately given a five-second penalty, effectively ending the race as a contest as Hamilton managed his tyres to seal one of the most famous wins of his career.