McLaren's Lando Norris was runner-up for the second straight race, but 33.731 seconds behind at the chequered flag on a hot afternoon at the Hungaroring.
Verstappen's teammate and closest title rival Sergio Perez had to settle for third after starting ninth and chasing Norris in the closing stages before the Briton built up more of a buffer.
The 44th career win was a ninth in 11 races so far this season for Verstappen, and seventh in a row, stretching his lead over Perez to 110 points with the double world champion also taking the fastest lap.
"What an unbelievable rocket ship that was today. That was so enjoyable to drive. Unbelievable," said Verstappen over the team radio.
"We could do basically whatever we wanted with the strategy. Twelve in a row for the team is pretty incredible."
Verstappen called it "a pretty perfect day", although the porcelain winner's trophy failed to make it through the podium celebrations intact after Norris sent it tumbling off the top step when he cracked open the champagne.
The run of 12 wins, a tally that includes last season's final race in Abu Dhabi, beat McLaren's 11 in a row in 1988 recorded by greats Alain Prost and Ayrton Senna.
Although Ferrari won 14 successive races that they entered in 1952-53, the Italian team did not compete in the Indianapolis 500 which counted as a round of the championship at that time.
Verstappen's winning margin was the biggest since Mercedes' seven-time world champion Lewis Hamilton won in Russia in 2021 by 53 seconds.
HAMILTON POLE
Hamilton ended up fourth, after the eight-time Hungarian GP winner had started on pole for the 104th occasion in his career and first since 2021. He narrowed the gap to Perez over the closing laps but ran out of time.
McLaren's Australian rookie Oscar Piastri finished fifth.
George Russell was sixth for Mercedes, after starting 18th, with Ferrari's Charles Leclerc and Carlos Sainz seventh and eighth.
Leclerc finished sixth on the road but lost a position due to a five-second penalty for speeding in the pitlane.
Aston Martin's Fernando Alonso and Lance Stroll filled the final two scoring places.
Verstappen seized the lead at the start from Hamilton, who dropped to fourth after also losing out to both McLaren drivers with Piastri sweeping around the outside and into second.
The upgraded Red Bull then showed it was in another league entirely, Verstappen pulling away and leaving others to fight for the remaining places.
Perez, under pressure after failing to make the podium in four of his last five races, had a good afternoon after starting on the hard tyre while others were on mediums and making some aggressive overtakes.
"His recovery and overtaking was brave, his pace was fast. The way he made the places - passing Carlos, passing Fernando, passing Piastri, the strategy that he had. He was on fire today," said team boss Christian Horner.
"A race like that only gives you a huge amount of confidence. For me, that was a statement drive to say 'Don't write me off'."
Alpine drivers Pierre Gasly and Esteban Ocon collided at the first corner of the opening lap and retired in the pits, dealing the Renault-owned team a second successive double-blank.
Alfa Romeo's Guanyu Zhou made a slow getaway from fifth place with the Chinese then hitting Yuki Tsunoda's AlphaTauri and triggering a chain reaction that pushed the Alpines together.
Australian Daniel Ricciardo, making his return with AlphaTauri, was also caught up in the chaos and dropped from 13th to 18th before finishing where he started.
Zhou was handed a five-second penalty for causing the collision.
