Martin finished ahead of KTM's Brad Binder and Ducati's Bagnaia after an intense battle for the top three spots where they constantly swapped positions in the last two laps.
But Binder was demoted a position for exceeding track limits on the final lap, putting him third, behind Bagnaia.
The battle for podium spots was the fourth-closest finish in premier class history as the top three finished within 0.253 seconds of each other.
"I'm so happy, this feeling is amazing. Today I didn't have better pace than them. I had to put in more than 100%," Martin said in a post-race interview.
"The pace was great, tyre management was great. The hard moments are tough but they make you stronger."
Martin set a lap record when he secured pole on Saturday and led from start to finish, claiming his fifth straight sprint victory of the season.
Just as in the sprint, Martin kept Luca Marini at bay going into turn one as both Ducatis shot off the line.
Bagnaia, starting sixth on the grid, struggled to find a way past early on. He had his hands full with Honda's Marc Marquez, who pushed the world champion down to seventh.
Binder finished second in the sprint and the South African soon found the pace to move up and sit behind Martin as the pair slowly pulled away from the pack while Gresini Ducati's Alex Marquez slotted in at third.
Bagnaia then found his groove and set the race's fastest laps, picking his way through to move up to fourth. The Italian was gifted third place when Alex slid off at turn 10, his Gresini bike cartwheeling through the air when it hit the gravel.
Bagnaia still had a half-second gap to close but he had a front-row seat to a tussle for the lead between Binder and Martin as the pair swapped places on consecutive laps before the KTM rider finally took the lead with four laps to go.
On the penultimate lap, Martin saw a gap to make a daring overtake on the inside and Binder had no choice but to concede the lead as the Spaniard held on to take the chequered flag.
Bagnaia, relieved to move up from seventh to finish second, will hold a slender championship lead with three races to go this season in Malaysia, Qatar and Valencia.
"In the last few laps, I was feeling like I was in a game," Bagnaia said. "Finishing second considering the championship and where I was at the start (of the race), I'm very happy overall."
