Following his pit stop on lap 31, Lewis Hamilton rejoined the race still second, 6.2s down on the leader and 7.9s ahead of Vettel, who had yet to stop.
Setting a string of fastest laps, the Briton closed to within 1.7s of Verstappen, at which point the Red Bull driver was warned: "Hamilton is behind, expect him to attack while his tyres are fresh."
And attack he did.
As they worked their way through the backmarkers, Hamilton looked here and there, seeking out the perfect opportunity to make his move.
Finally, the Briton made a move in Turn 4, and actually got ahead of his rival, but ran wide in the process.
"Keep the pressure on," Hamilton was told. "I can't keep the pressure on," he insisted, the Briton by now worried about his brake temperatures.
"You need to give me full power," snapped Verstappen. "You've got full power," came the worrying reply.
As the Red Bull driver asked to be advised when his pursuer had DRS, Hamilton was told "let's just close right up".
And then it happened. On lap 48, moments after his teammate and Ricciardo had stopped, Hamilton pitted for a second time. As he rejoined the track he was 20s down on the Red Bull.
The rest is Formula One folklore, and something that those keen on betting on sports probably took a punt on .
"It will be interesting when we go back and talk about the two stop," Hamilton told reporters after the race, "because today, this morning, we talked about the strategy and they said two stop was not going to happen, and even when we called to do a two stop, I was like Jeez, I don't know how this is going to work.
"A gamble's always a good thing," he continued, "and it felt like a big gamble for us, but at the time I felt like I had the pace on Max. I don't know if he was backing off, or he was just controlling the pace but I felt like OK, I'm going to have a few attempts at trying to pass him but at some stage the tyres are going to go off, so I don't know how many attempts that will be.
"I really don't know how long I made those mediums go but I think it was just a collectively… a really bold, risky strategy call and then just doing the job", he added, strategist James Vowles effectively putting it all on black with online casinos america.
"At the end of the day, I had to do those laps to chew out the gap that he had on me so I think collectively, as a team, we did a really exceptional job.
"You have to put complete faith in your team," he added, "because they have different viewpoint to you, so we did the stop and I came out on the mediums and I thought 'Jeez, I don't know if these are going to go the distance at the speed I am going to have to go'. Also Max turned up the engine mode and they started doing mid-19s. I started thinking 'I don't know if I'm (going to) close this gap'.
"I think the trajectory, they said I was going to catch him with nine laps to go and then that changed super quickly and went to last lap. So after that I had to put all doubt and all question marks out of my mind and go for the best laps I could do every single lap and consistency and not drop any time whatsoever.
"I had one of the most consistent period of laps that I'd had. I don't know if he had traffic or mistakes or whatever but the gap started to chop down quite quickly. With four or five laps to go I had him four seconds ahead and I could see him in my sights, so maybe he's struggling with his tyres. So after that I was like 'OK, we've got a serious race on here'.
"It felt like the steepest wall to climb when you come out that far behind but the team had relaxed faith that we would do it and I'm grateful for their hard work and the decision."
Check out our Sunday gallery from the Hungaroring, here.