The pair emerged as class of the field after a frantic opening to the Austrian Grand Prix and fought it out for victory, Dovizioso prevailing by 0.176s despite a desperate last-corner lunge by his rival.
Having won the last two Global Positioning System, three-time world champion Marquez has a 14-point lead in the standings over Maverick Vinales, who was fourth on Saturday with his Yamaha team-mate Valentino Rossi seventh.
Dovizioso was not happy with how Marquez tried to force his way through on the inside of Turn 10 though as he gestured towards him, with the Spaniard's Honda sliding out of control as he ran wide allowing Dovizioso back through to take the win and add to his earlier successes at Mugello and Barcelona.
It was a disappointing start and finish for Marquez, who was passed by Lorenzo on the first lap after beginning on pole. However, that was just a temporary push as the Honda rider charged back into taking second place.
Marquez retook the spot shortly thereafter at Turn 7, but again couldn't shake Dovizioso - who slipstreamed past on the main straight with seven laps to go.
Although Johann Zarco and then Marquez knocked Rossi off top spot at the halfway point, the Italian went quicker again and became the first rider to beat Andrea Dovizioso's Friday benchmark by going under the 1m24s barrier.
On that lap, they traded places several times, Marquez not managing to make a move stick and easing the pressure on the Ducati for a few laps afterwards. The last corner was completely on the limit, but this is MotoGP.
Marquez lunged down the inside of the Italian, with both forced wide but Dovizioso getting a better exit to hang on to victory.
Marquez recovered to finish second ahead of Honda teammate Dani Pedrosa, with Lorenzo coming home in fourth after fading from the battle at the front early on. Aspar Ducati's Alvaro Bautista finished 8th with Avintia Ducati's Loris Baz finished 9th.
Last year's victor Andrea Iannone will start 10th on the grid after finishing nearly a second off the pace on his Suzuki.
Australia's Jack Miller crashed out on lap nine of the race.
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