The Italian Ducati rider, who qualified second on the grid after dominating practice and winning the sprint on Saturday, overtook Prima Pramac Racing's Martin on the second lap.
Having smashed the lap record to take pole position at the Red Bull Ring in Spielberg on Saturday, Martin finished second. Enea Bastianini came third to complete an all-Ducati podium.
Bagnaia's victory moved him up to 275 points, five more than Martin, with Bastianini maintaining his hold on third place on 214.
"The pace was incredible. I think Jorge and I did something unbelievable in terms of speed and consistency," Bagnaia told reporters.
"I was just trying to do a little better than him every lap to open a gap because I knew that in the last laps, anything could happen here with the rear tyre.
"But I'm very happy... I want to say thanks to all my team and to the academy for the work they are doing every day. It's a special day for us."
There was no stopping Bagnaia once he had clear road ahead of him as Martin struggled to match his pace. Bagnaia crossed the finish line well ahead of the chasing pack to win his third consecutive Austrian Grand Prix.
Six-time MotoGP champion Marc Marquez, third-quickest in qualifying, made up several positions to finish fourth after getting off to a poor start by going wide in the opening lap.
The 31-year-old had also crashed out of the sprint and now sits fourth in the championship standings.
