Hamilton took the lead from team-mate Valtteri Bottas off the line but was left vulnerable when his rivals all pitted during the early virtual safety auto period while he stayed out on track.
Having dropped to fourth, Hamilton then had to park his auto on the 64th lap, seven short of the finish.
The points moved Haas up to fifth overall after the team's 50th race. I feel fine about it.
"It was absolutely nailed in the first lap". The VSC doesn't go more cruel for us.
Red Bull driver Max Verstappen of the Netherlands takes a curve followed by Ferrari driver Kimi Raikkonen of Finland, right, and Red Bull driver Daniel Ricciardo of Australia during the Austrian Formula One Grand Prix at the Red Bull Ring racetrack in Spielberg, southern Austria, Sunday July 1, 2018.
While Barcelona saw Hamilton and then teammate Nico Rosberg collide in 2016, Mercedes has not had a double retirement due to reliability issues as a constructor since the 1955 Italian Grand Prix.
Hamilton had topped both sessions on Friday and both he and Bottas posted fastest laps in Saturday's practice before Vettel hit back to take the initiative. "I have every confidence in my team that we'll be able to bounce back".
"We did a good job and a good race", says Vettel. "The situation is different this year, we are fighting, six cars, and that is just a tough situation". "The auto has been great, we were quickest". It's very rare and incredibly unusual for us to have these two DNFs in one weekend.
Mercedes had half a lap to react and while others came in for fresh tyres, Hamilton stayed out. "This is where we lost the race". The Englishman has masterminded the tactics at Mercedes for all their recent success, but he has now overseen three strategical errors which could cost Hamilton the title.
"Lewis, this is James". 'We understand. It's my mistake, ' before later adding: 'I have thrown away the win.
Vowles subsequently twice spoke to Hamilton directly, apologising for the mistake and trying to motivate him, saying "Give us what you can", and later, "We trust in you and believe in you".
"For Lewis, he was leading comfortably and then he was in fourth".
"This is a great result for the team, and Valtteri deserves that", he insisted. "That's what got me invested in racing and really caught my heart, it's where the passion is", Hamilton said.
"Just thrown away a win". "We need to find a bulletproof method to move forward for strategy because if our vehicle had kept going it was an easy win for us, we were comfortably ahead".
"Last weekend with the new engine it was positive but, even with the engine, between us and Ferrari the margins are very small".