Eventually he made a stop 10 laps later to limit the damage.
He was then perfectly placed as Bottas and later Lewis Hamilton both retired with mechanical issues, while Verstappen's team-mate Daniel Ricciardo was also forced to stop out on track.
The Finn had started from pole, his first of the season, but lost out to Hamilton at the start and dropped to fourth before fighting back to second.
"It was incredible", said Verstappen. And a really very mature drive from him to make sure he had just enough left in the last five, ten laps, because Ferrari were probably better than us on tire deg.
The Dutchman secured the team's third victory of the season and the first for Red Bull at their home race at the Red Bull Ring.
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An official quick-count revealed that Lopez Obrador took the lead with 53-53.8% of votes, according to the electoral authority. In June, Obrador called for a flood of immigrants to enter the U.S.to protest the border crisis and claim their "human right".
It was an important victory for Verstappen, who had been heavily criticised in the opening six races of the year for a string of messy crashes that cost him points and a potential victory in China. The Aussie knows that at some point he will need to take fresh parts.
Verstappen is in fifth place overall, 50 points behind Vettel with almost half the season gone, but he told Sky F1: 'We need a bit more engine power and then we can definitely be in the mix'.
"I was surprised, it was pretty much a given", Horner said about Mercedes' decision and the call to pit under the VSC in general.
Raikkonen took second place after a week of febrile speculation that he is destined to be replaced by Charles Leclerc, perhaps as early as August.
"It's really great to see the updates", four-time champion Hamilton said.
"The soft tyre fell apart".
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A mural of Argentina's Lionel Messi is painted next to another of Portugal's Cristiano Ronaldo in Kazan June 29, 2018. We don't need to describe him.
"From my side I felt in control, I was driving to the best I could with the auto I had and at the end we were struggling a little more than Ferrari with the tyre blistering but we managed to stay ahead". "It's a shame, we had a great vehicle today".
"Obviously it would've been nice to start further up", he said.
"I tried to get some [places] back at the start but was left with nowhere to go and it was the same at Turn 3", Vettel said.
The result was particularly important for Grosjean, who had hitherto failed to score a point through a series of critical driver errors.
Meanwhile there were double points finishes for both Haas and Force India, but it was another disappointing weekend for Williams and McLaren.
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However, in the final minute of stoppage time, Colombia defender Yerry Mina equalised to take the match into extra-time. Courtois said afterwards: "The goalkeeper is 10cm smaller than me".
The triple-header of consecutive French, Austrian and British races concludes next week at Silverstone with the championship now fascinatingly poised.