In a pulsating encounter, which saw the lead change hands on several occasions, Petrucci picked his moment in the final lap to deny championship contenders Marquez and Dovizioso.
"It's unbelievable, in the best place of the world," said Petrucci, who finished eighth in the 2017 and 2018 world championships.
"It was a fantastic race. I cannot describe the feeling I have now because I have not recognised that I have won. Now when I jump on the podium I think I will realise.
"For sure I would like to thank my family, my friends, and all the people in Ducati. And also Andrea Dovizioso for helping me through the winter and this season. This win is for everyone who helped me."
Championship leader Marquez moved up to 115 points in the overall standings, ahead of Dovizioso (103) and Suzuki's Alex Rins (88), who finished the race in fourth place.
"My goal was to finish in front of Dovi, finish in front of Rins, in front of Valentino (Rossi) - we did, so I'm happy with these 20 points in Italy," Marquez added.
French rider Fabio Quartararo, who started second on the grid, made a dismal start to the race and slipped down to eighth spot in the opening lap and could only finish 10th on his Petronas Yamaha.
It was an even worse day for Rossi who was running 15th when he got tangled up with Joan Mir's Suzuki, with both riders running across the gravel.
The nine-times world champion went down to 21st before he crashed after 16 laps on turn nine and was forced to retire.
(Reporting by Hardik Vyas in Bengaluru, editing by Pritha Sarkar)
