The 30-year-old Italian started on pole but was forced to scrap for his victory in a thrilling race, crossing the line in 42 minutes, 27.333 seconds ahead of Rossi (42:30.448) and his Yamaha team mate Jorge Lorenzo (42:39.257).
World champion Marc Marquez, who clinched his third title in Japan two weeks ago, came off his Honda for the second week in a row but rejoined the race to finish 11th.
Dovizioso's team mate Andrea Iannone was less fortunate and his race-ending crash meant he failed to get any reward for the ding-dong battle with Rossi which lit up the first half of the race.
Iannone had missed the last four races after suffering a fractured vertebra in practice for September's San Marino Grand Prix but, after heavy rain had delayed the start, took an early lead from the second row of the grid.
Rossi was hard on his back wheel, though, and the lead went back and forth between the two Italians until Iannone came off with seven of the 19 laps remaining.
Dovizioso took up the challenge for Ducati and hit the front when Rossi went wide at turn one five laps from the end before racing away for his second victory in MotoGP, seven years after his first at the British Grand Prix.
The Italian was particularly pleased with the victory after finishing second behind Iannone at the Austrian Grand Prix earlier this year.
"That victory was mine but I made a bad decision and I was very, very disappointed because I thought I rode in a perfect way," he said.
"To get a result now, this year, before the end of the season was very important."
LCR Honda's Cal Crutchlow was another faller from fifth place, ending his quest to become the first British rider to win back-to-back races since Barry Sheene in 1977 after his Australia triumph last week.
Rossi's finish ensured the nine-times world champion will finish second in the riders' standings ahead of 2015 champion Lorenzo, whatever the result of the final race of the season in Valencia on Nov. 13.
Earlier, Johann Zarco retained the Moto2 title after a dominant victory on his Kalex gave him a sixth race win of the year.
Zarco, who moves up to MotoGP with Yamaha next year, was the first Frenchman to win two grand prix world championships.
(Writing by Nick Mulvenney in Singapore, editing by Sudipto Ganguly)
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