Verstappen was unhappy with his car for much of the race, but Red Bull pulled a masterstroke when they fitted soft tyres to his car at his second pit stop.
The aim was to challenge Hamilton in the later laps after the seven-time champion made an early second stop with 40 laps still to go.
It was heading towards a tense climax when Piastri’s retirement brought out the VSC.
That prompted a late round of pit stops, Ferrari bringing in both their drivers and putting them behind Verstappen.
Hamilton came out of the pits and passed Antonelli into the first corner, after the Italian stayed out under the VSC, but had to give the place back after the restart because the Mercedes driver had just passed the key line on the track in front.
Antonelli and Hamilton started chasing back towards Verstappen, but they were delayed while lapping Audi’s Gabriel Bortoleto.
That looked as if it might be decisive, but in the end Verstappen was comfortably able to keep Antonelli at bay, crossing the line 3.6 seconds ahead.
Another key point in Verstappen’s race had been his re-passing of Hamilton after the Ferrari had got briefly ahead following the first pit stops.
That gave him clear air and enabled the Dutchman to consolidate his race position in third place behind the McLarens, laying the foundations for Red Bull’s late strategy call.
Hamilton will leave Hungary ruing another penalty – the one for speeding in the pit lane was his second in two days after behind penalised for blocking Piastri in qualifying, and follows two other penalties at the previous two races in Belgium and Britain.
Behind him, Red Bull’s Isack Hadjar was sixth, ahead of Russell, who dropped to 21st place on the first lap after his anti-stall kicked in at the start, and fought back strongly.
At Aston Martin, Lance Stroll finished in 13th, ahead of team-mate Fernando Alonso, their positions dictated to a degree by luck under the VSC and their divergent strategies.
But the key point was that Alonso, in particular, was able to fight with other cars for the first time, and he ran a long first stint on the soft tyres, before switching to the mediums, which was a bold strategy.
The long-awaited upgrade to their car, which was new apart from the front suspension, engine and gearbox, has reduced their lap times by about two seconds.
A Honda engine upgrade is due for the Dutch Grand Prix, the next race in four weeks’ time after the summer break, which the team hope will elevate them further and potentially bring the possibility of the occasional points finish into the picture.
