Verstappen was 24 seconds clear of Ferrari's Charles Leclerc in the closing stages of the Red Bull Ring race, which was just more than the time lost by pitting for fresh tyres.
But despite the close margins and the risk of losing the lead if the stop went wrong, Red Bull elected to pit the world champion for softs so he could snatch the fastest lap point on the run to the chequered flag.
The stop was brilliantly executed, and Verstappen was able to emerge still in the lead as he duly went on to grab the extra point.
Reflecting on the potential dangers of stopping when the margins were so tight, Red Bull team boss Christian Horner reckoned that the faith he had in his team to get everything right meant he did not feel it was too much of a gamble.
Speaking about the late stop, Horner said: "It was the first time we've been back here since Dietrich's passing, so it felt very poignant that it was a great team performance toady.
"We decided to go for the last lap, the fastest lap on the last lap, despite the risk involved in fluffing a pitstop. That [Mateschitz's absence] was in the back of my mind and his mantra was always no risk, no fun.
"But the mechanics have been in such great form, that it seemed a low-risk thing to do in the end."
Horner admitted that there had been some debate about the issue on the pit wall about what best to do, but in the end it was agreed that stopping was worth it.
"There was a bit of a discussion of risk versus reward," he explained. "We thought let's cool the tyres down and do it the easier way, of not taking the risk of a pitstop in which 400 things can go wrong in.
"Then Max was making his opinion quite clear that the tyres were f****d, and he was quite focused. So, then you start looking at your risk. Do we take the risk on a below-par set of tyres? Or is it actually less risk to take the pitstop and put on a set of softs?
"In the end, we said, 'Look, let's take the risk.' And he still had three seconds margin over Charles when he came out of the pitlane."
Speaking about his own mindset, Verstappen said he had no doubts that stopping was the better thing to do to help him grab an extra point.
Asked how much of a risk he felt it was, he said: "To me not, but to the team, I think they were a little bit more nervous.
"I saw the gap and I was like 'we have to pit; I want to go for the fastest lap'.
"From the outside maybe it looks like a big risk. But when you're in the car, for me, it didn't feel like a risk at all."
