Last year's victor Andrea Iannone will start 10th on the grid after finishing nearly a second off the pace on his Suzuki.
It proved to be a dramatic conclusion to an already thrilling and closely-fought race at the Red Bull Ring, with Dovizioso and Marquez involved in the lead battles throughout.
However, that was only a temporary setback, as Marquez was soon back into second and all over Lorenzo, forcing the Spaniard to go wide at the same corner.
However, Dovizioso ran deep into Turn 4 and dropped behind Marquez, before they both pulled away from Lorenzo - who was later passed by Dani Pedrosa.
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Dovizioso saw it coming and cut back inside the sliding RCV on the exit, casually waving his hand as he rode to what was surely the best victory of his career.
The session started with Yamaha's Valentino Rossi - who had struggled with illness on Friday and could only manage 12th in practices one and two - leading the early running.
Lorenzo's pace began to fade from that point onwards, yet Dovizioso managed to stick within a couple of tenths of Marquez and coasted past again when the reigning champion erred at Turn 3 on lap 18 of 28.
The Marquez-Dovizioso duel allowed Pedrosa to close right up to the pair, but he was unable to keep their pace and finished 2.485 seconds off.
Yamaha's Maverick Vinales produced a late recovery to climb up to fourth on the grid, with Ducati's Danilo Petrucci rounding out the top five.
Alvaro Bautista, Loris Baz and KTM test rider Mika Kallio rounded out the top 10.