The victory at Suzuka was the Dutch driver's 13th of the season and left him on the brink of a third world championship after Mexican teammate Sergio Perez, his closest rival, failed to finish.
McLaren's Lando Norris and Australian rookie Oscar Piastri, on a grand prix podium for the first time, finished second and third.
Verstappen, who also took the fastest lap and now leads Perez by a massive 177 points, can seal his third drivers' title in a row with five rounds to spare at next month's Qatar Grand Prix.
The constructors' title was Red Bull's sixth since they entered the sport in 2005 and they did it at a circuit owned by engine partner Honda.
"Max, that was absolutely fantastic," said team boss Christian Horner over the radio in congratulating Verstappen on a 48th career win and Red Bull's 15th of the season.
"Thank you very much, you were totally awesome and dominant this weekend."
Verstappen thanked the team in reply for the "unbelievable season" they are having.
"You can all be very proud here at the track and back at the factory. You have built a rocket ship of a car," he added, after taking the chequered flag 19.387 seconds ahead of Norris.
McLaren's first double podium of the season, with team orders ultimately deciding the positions on strategy, cemented their growing status as Red Bull's closest challengers on track.
"We're not close to Max but we are not miles away either so I'm very happy," said Norris. "We're getting there. We are pushing and the progress we have made is pretty outstanding."
Ferrari's Charles Leclerc finished fourth with seven-times world champion Lewis Hamilton fifth for Mercedes and Carlos Sainz, winner of the previous race in Singapore, sixth in his Ferrari.
George Russell took seventh for Mercedes ahead of Aston Martin's Fernando Alonso and the Alpine pair of Esteban Ocon and Pierre Gasly.
Verstappen defended against the McLarens at the start, with Norris seizing the opportunity to pass Piastri and slot into second place.
Behind them there was immediate chaos, with the safety car deployed due to debris on track after a number of clashes including Perez and Hamilton.
Perez pitted for a new front wing but collected a five-second penalty for an infringement of the safety car rules, and his race went from bad to worse when he then collided with Haas's Kevin Magnussen on lap 12.
The Mexican pitted again for another front wing, taking his penalty and returning in last place before being slapped with another five-second sanction for the collision and stopping in the pits on lap 15.
Perez then returned to the track nearly an hour later, and with 13 laps remaining, to serve the penalty and avoid the risk of a grid drop at the next race.
His final retirement ended Red Bull's 100% finishing record for the season.
