Mercedes had the quicker car in Budapest, but the twisty Hungaroring forced Mercedes to deploy an alternative strategy to aid Hamilton’s way past the polesitting Dutchman.
Verstappen did little wrong in defeat, nailing his start to hold the lead while Hamilton and teammate Valtteri Bottas, starting third and second respectively, battled for the right to take him on.
But the fight didn’t end cleanly. Hamilton swept around Bottas’s outside at turn two, but the Finn damaged his front wing by clipping the Briton’s rear wheels in defence. He was forced to stop for repairs, eliminating him from podium contention.
Mercedes’s tactical numerical advantage was erased, leaving Verstappen and Hamilton to engage in a one-on-one battle for the lead. They held station early with a gap of around two seconds, but by lap 20 the Red Bull Racing car’s tyres started expiring and its pace slowed.
Verstappen stopped on lap 25 before Hamilton could reel him in, switching to a new set of hard-compound tyres. Hamilton, however, held back for six more laps in the hope fresher tyres could make the difference in the second stint.
He emerged from pit lane on lap 32 with an almost six-second deficit, but on new tyres the Mercedes came alive, slashing the gap to nothing after only two laps.
The Briton bided his time as he and Verstappen shuffled through lapped traffic before striking on lap 38. They dived side by side into turns two and three, but just as Hamilton appeared to get his nose ahead he ran wide on the outside of turn four, forcing him to concede the place.
The best of Hamilton’s tyres had been expended and Verstappen had forced a stalemate — until Mercedes pulled a blinder, pitting Hamilton for a new set of medium-compound tyres at the end of lap 48.
The Briton had 21 laps to close the 20-second deficit to Verstappen, and though the gap started closing only slowly, in 15 laps he was within striking distance.
Verstappen knew the game was up, radioing his team that his tyres were dead, and on lap 57 the inexorable Hamilton slithered past his ailing rival into the first turn, taking the lead and confirming his eighth win of the year.
“For a race to be able to push like that—I’m telling you, it was on the limit all the way,” Hamilton said exuberantly. “I just kept pushing and the gap closed. The laps were like qualifying laps.
“I honestly didn’t know if I could catch [Verstappen]. Like the team said, just keep your head down, and I did.
“I feel really grateful for the day and really for the team for continuing to believe in me and continuing to push to the limits and take a risk and a chance on me.
“If it wasn’t for these boys here and all those back at the factory, this wouldn’t be possible.”
Verstappen was circumspect out of the car, acknowledging that his team had been outfoxed, though the Dutchman was at least able to score a consolation point for fastest lap after pitting for a set of soft tyres after losing the lead to Hamilton.
“We were just not fast enough,” he said. “I tried everything I could on that hard tyre to stay alive, but unfortunately it wasn’t enough.
“He was pushing me very hard. I like that.
“Still, second place, fastest lap—a good weekend overall for us.”
With Bottas out of the frontrunning picture, Sebastian Vettel’s way was clear to finish third for Ferrari after passing teammate Charles Leclerc on lap 68 of 70.
The German was equipped with the faster strategy, ending the race on the soft tyre rather than the hard, but his 61-second deficit to Hamilton meant the result was bittersweet.
“We couldn’t go at the pace with these two, that was quite clear the whole weekend,” he said. “A lot of work ahead of us.
“We need maybe to charge our batteries and then the battle continues. Overall we need to get stronger.”
Carlos Sainz finished a fantastic fifth for McLaren after fending off Red Bull Racing’s Pierre Gasly, defeating the Frenchman in the far faster car by just 1.393 seconds.
Gasly had endured another dreadful day. He dropped to ninth off the line, recovering to sixth principally through the misfortune of others — he tactically overcut Kimi Raikkonen, but Bottas was affected by his first-lap damage and Lando Norris lost places with a slow pit stop.
Raikkonen finished less than three seconds behind in seventh for Alfa Romeo, the Finn doing well to keep compatriot Bottas at bay by only 0.736 seconds at the flag despite the Mercedes driver ending the race on the faster medium tyre.
Norris took home two points from ninth for McLaren ahead of Thai driver Alex Albon in 10th for Toro Rosso.