Having clinched pole with a lap record after going fastest in practice and qualifying, Bezzecchi was slow getting away when the lights went out while Bagnaia turned on the aggression as soon as he shot off the line.
Bagnaia elbowed Bezzecchi out of the way at the first turn, which also allowed Red Bull KTM's Brad Binder to move up to second, dropping the pole sitter to third.
But Bezzecchi recovered to overtake Binder and set a fastest lap as he battled with Bagnaia for top spot, crawling all over the red Ducati.
His pressure finally paid off as he eventually found a way past the world championship leader to retake the lead.
Once he was through, Bezzecchi put the hammer down and extended his lead to nearly a second but Bagnaia did not give in and made his fellow Italian work for the win over the course of 13 laps.
"I felt amazing today on the bike. I made a mistake on the first corner and lost two places, but fortunately, my pace was good to have a fight with Brad and Pecco (Bagnaia)," Bezzecchi said.
Behind them, Binder was involved in a battle with Yamaha's Fabio Quartararo and he pumped his fist in celebration when he crossed the line in third. But elation turned to dismay when he found out he had received a time penalty.
The South African had exceeded track limits by mere inches on the final lap and because he could not serve a long lap penalty, he was demoted to fifth with a three-second time penalty to give Quartararo the final podium spot.
"I'm feeling sorry for Brad, it happened to me a few years ago," Quartararo said. "I couldn't pass Brad but hopefully in tomorrow's race I can have a better start."
