Hamilton, quickest in both sessions on Friday, has claimed pole for the past two years in Austria, and has also started from the front for three of the last four Grands Prix of 2017.
Three-time world champion Hamilton recorded his best lap at one minute, 05.975 seconds at the Red Bull Ring circuit - 0.190 seconds faster than 19-year-old Dutch Max Verstappen (Red Bull), reports Efe.
"It was a smooth day generally", Hamilton said. "The vehicle feels really good all around the lap".
"This track punishes you if you make a mistake, and I tested those limits", added Bottas.
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Verstappen, fourth fastest in P2, said his tires were "all over the place" in the afternoon. However, the Spanish driver was also one of several to spin on turn six, and again on turn seven and into the gravel.
Hamilton's problem meant he returned to the track behind Vettel and was unable to pass.
Further back, Lance Stroll, Felipe Massa, Pascal Wehrlein, Daniil Kvyat and Carlos Sainz all came off the track at various points as they struggled for grip, while Romain Grosjean's wide run at Turn 9 saw him suffer a puncture for his troubles.
Vettel was given a time penalty during that race but escaped further punishment from the FIA, motor sport's governing body, following a hearing on Monday (Tuesday NZT).
Bottas, who has reiterated his Formula 1 world title charge having closed the deficit to 42 points on Vettel thanks to his back-to-back second places, is exclusively focusing on pole position in Austria as he looks to take on Vettel and Hamilton who have largely dominated the sharp end in 2017.
Championship leader Sebastian Vettel was fourth, 0.449s off title rival Hamilton, and was one of the cars to spin early in the session after losing the rear of his auto on the Turn 1 apex.