What looked like a straightforward Verstappen victory from pole came undone before the end of the lap, when a downpour forecast for later in the race arrived ahead of time.
The Dutchman delayed his pit stop for wet tyres until the end of the second lap, but the slow reaction time meant he dropped briefly to as low as 13th in the chaos before recovering to fourth and quickly rising back to second.
The new leader was teammate Sergio Pérez, who had astutely switched rubber at the end of the first lap and found himself with an almost 15-second lead over the home favourite once the pit stops were done.
But Verstappen was on a charge, and by lap 11 he was only three seconds adrift of the leader and considering his options for a pass.
By then the rain had stopped, however, and slick tyres were faster once again. Fernando Alonso, who had gained a pair of places off the line to run third, was first in among the top three.
Sensing an undercut threat, Red Bull Racing pulled Verstappen in first. He comfortably covered the following Spaniard, and his advantage on fresh dry-weather rubber was so great that Pérez rejoined behind him when he made his own stop just one lap later.
Red Bull Racing denied favouritism played a role in the decision-making, though the happy side-effect was not having its drivers battle for position in the sketchy conditions.
Verstappen looked to have the race sewn up with a 10-second advantage with 12 laps to go when the heavens opened once more.
All drivers pitted between laps 60 and 61 for new tyres, but this time the rain was far more intense.
Pérez locked up at the first turn and lost second place to Alonso, but further back Zhou Guanyu wasn’t as lucky, spearing into the barriers and bringing out the red flags.
The race was suspended for almost 50 minutes to recover the unhurt Chinese driver’s car and to wait for conditions to improve. The race got back underway with a rolling restart and just five racing laps remaining.
Despite some inquiries from Alonso, Verstappen held the lead comfortably in the slick conditions to finally secure victory after 72 laps.
“Incredible,” Verstappen said. “Today they didn’t make it easy for us with the weather to make all the time the right calls. But I’m incredibly proud.”
The win extends Verstappen’s lead to 138 points and sets him up to potentially win the championship as early as in Japan in three races time.
Alonso resumed the season in strong form, with a muscular first lap setting him up for his first podium since June in a revised Aston Martin car that the team hopes will return it to regular top-three contention.
“It was a very intense race,” he said. “The car was flying today - very competitive, very easy to drive.
“In these conditions, you need a car that you can trust, and I did trust the car a lot today.”
Pérez should have secured at least a podium, up from seventh on the grid, thanks to his strong call to pit on the opening lap, but the Mexican locked up on his way to the pits for the red flag and was found to have broken the pit lane speed limit, incurring a five-second penalty.
Pierre Gasly, who had also made big gains with some well-timed stops at the start of the race to rise from 12th to fourth, clung to the back of the Red Bull Racing car in the final five laps to ensure he could capitalise on the punishment, securing a rare rostrum appearance for the beleaguered Alpine team.
“I’m feeling so stoked,” he said. “Obviously I tried to push as hard as I could to stay within five seconds and managed to do it.
“It was a very long race, very challenging from start to finish, and it was greatly executed from all the guys.”
Pérez finished fourth ahead of a battle for fifth between Carlos Sainz, Lewis Hamilton and Lando Norris, with the Ferrari driver prevailing on an otherwise uncompetitive weekend for the Italian team.
Thai driver Alex Albon was a strong eighth for the backmarker Williams team as one of only five drivers able to keep their cars on the road without changing to wet tyres in the opening phase of the race, a decision that eventually swung back in his favour after the early chaos.
Oscar Piastri finished close behind him after likewise eschewing an early stop, while Esteban Ocon completed the top 10 for Alpine.