With the following grand prix at Silverstone, where Hamilton has been dominant with four wins from the past four races, extending his lead further at the Red Bull Ring would put him in a commanding position going into the final European races, where he has traditionally been strong.
"It was awesome", Verstappen said.
Ferrari now sits atop the Constructors' Championship, 10 points ahead of Mercedes, in addition to Vettel's Drivers' Title catapult.
A seething Hamilton said: "I want to say something, but just leave me to it".
At the start, Raikkonen made a rapid departure from third to dive between the two Mercedes as Bottas struggled uphill and Hamilton took the initiative.
Details of Hamilton's retirement have emerged as the radio conversation between the Mercedes team became available - with auto problems and a major strategy error to blame.
Hamilton dropped to fourth, and following a series of furious exchanges with the Mercedes pit wall, he then ran out of power with only seven laps remaining.
He said: "We don't need to make changes". Kimi was pushing as hard as he could, I was pushing as hard as I could, the both of us were catching, but not enough. I tried to get some [positions] back at the start at Turn 1 but it didn't quite work.
"It was hard racing but good racing, " he said.
"We can not throw away points".
Bottas was the first Mercedes driver to quit with a hydraulic defect to his gear box in lap 14.
In the ensuring virtual safety auto period, Ferrari and Red Bull cars pitted but Mercedes didn't.
Daniel Ricciardo, the Dutchman's Red Bull team-mate, and Mercedes' Lewis Hamilton were forced into emergency second pit stops yet Verstappen managed the soft tyres he took on at his only stop for 56 laps.
He subsequently pitted and rejoined in fourth, then had to stop again when his rear tyres blistered.
Mercedes' chief strategist, James Vowles, took the blame and was quick to say "sorry" to Hamilton over the radio.
With track temperatures significantly higher than during practice and qualifying in previous days, tire management became tricky.
Mercedes have brought aerodynamic improvements to Austria, after a new engine was introduced at the previous race in France which Hamilton won. After bumping into Bottas after the start of the French GP last week - and restarting his race from the back of the pack - the mishap this time happened in qualifying, with Vettel picking up a three-place grid penalty for impeding Renault's Carlos Sainz. "All we can do is move forwards and I am looking forward to them getting the vehicle back and trying to understand what the problem is and I know the guys will be working hard to rectify it and make sure it doesn't happen again". "It was damage limitation but the pace was very good and the tire management was very good".