Hamilton sustained damage after running on the kerbs at Turn 10, dropping from runner-up to fourth.
The seven-time world champion is now 32 points behind Verstappen following the Dutchman’s commanding win at Spielberg’s Red Bull Ring.
Hamilton was running in second for the majority of Sunday’s 71-lap race but was unable to keep Bottas and Norris behind as he nursed his wounded Mercedes.
Initially, Bottas was told by the Mercedes pit wall not to race Hamilton, hoping their star driver would be able to hang on to second and limit the championship damage to rival Verstappen.
But with Norris breathing down Bottas’s neck, Hamilton was asked to concede the position with 19 laps remaining.
Two laps later, Norris – on the most impressive afternoon of his three-season Formula One career – moved on to Hamilton’s gearbox before striking with a fine move at the left-handed sixth corner. The world champion pitted at the end of the lap and his chances of a podium finish were over.
For Verstappen, there were no such worries as he cruised to his fifth win in nine races.
After holding off Norris on the run down to the opening corner, the Dutchman never looked back and his victory was greeted with huge cheers from the 60,000-strong Red Bull Ring.
“It is incredible for everyone to have delivered this,” said Verstappen following his 15th career win. “Today has been amazing. It was insane to see all the fans and so much orange. It is great motivation for me, too.”
Hamilton started fourth and was in the same position at the end of the first lap.
The safety car was deployed after Esteban Ocon was forced to park his Alpine following a collision with Alfa Romeo’s Antonio Giovinazzi.
The safety car pitted at the end of lap three with Sergio Perez dropping down the order following an ambitious move on Norris.
The Mexican accused Norris of pushing him off the road at turn four as he ran through the gravel, falling from third to 10th, and the McLaren driver was dealt a five-second penalty.
Hamilton passed Norris for second on lap 20 of 71, hailing the performance of his fellow Briton on the radio. “Such a great driver, Lando,” said Hamilton.
Norris’s race engineer Will Joseph informed the young Briton of his penalty. The 21-year-old responded: “For what? What did the guy expect trying to go round the outside?”
Norris served his penalty at his stop allowing Bottas to leapfrog him. Norris dropped back to fourth but passed a wounded Hamilton to claim his third podium of an impressive campaign.
Norris said: “It was a lot of fun, a good race, but I am disappointed because we should have been second.
“I thought lap one was just racing. He tried to go round the outside which was stupid. He ran off the track himself and I did not push him. I am frustrated but happy with third.
“It is the first race I have been able to race a Mercedes and hopefully we can keep it up.”
Perez finished fifth ahead of Ferrari driver Carlos Sainz and McLaren’s Daniel Ricciardo. But Perez, also hit with two five-second penalties for forcing Charles Leclerc off the track twice, was demoted to sixth, promoting Sainz one place.
George Russell missed out on his first top-10 finish for Williams after Fernando Alonso passed him with three laps remaining. The Englishman took 11th.
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