Starting fourth on the grid, Marquez shadowed Bagnaia for much of the race before making his decisive move on lap 16.
He then pulled clear in the closing stages to secure the win after a controlled final stint, sealing back-to-back victories after also triumphing in Hungary earlier this month.
Bagnaia, who had been chasing his first double victory of the season after winning Saturday’s sprint, was unable to respond and was later overtaken by pole-sitter Ai Ogura of Trackhouse Racing on lap 18 while pushing to reel Marquez back in. Ogura finished second, 0.421 seconds behind Marquez.
The win put the Spaniard, fourth in the Championship standings, 40 points behind championship leader Marco Bezzecchi, who was suspended from Sunday's race after an altercation with a marshal following a crash during Saturday’s sprint race.
"It's a very important victory. I never give up," Marquez said.
"In the last lap, I was suffering a bit, but I just tried to keep the pace. I saw that Ogura was pushing me, but it was not enough. They were the longest six laps of the year so far for me."
Bagnaia came in third, despite coming under late pressure from VR46 Racing Team’s Fabio Di Giannantonio, who finished fourth. KTM’s Pedro Acosta retired from fifth with a technical issue in the final lap, handing the position to Honda HRC's Joan Mir.
"I was quite comfortable when I was leading, but the pace was not enough," Bagnaia said.
"I tried to make a comeback in the last few laps to improve my pace. But in any case, I am happy with the result."
Bezzecchi’s teammate Jorge Martin was the only rider still in mathematical contention for the championship lead, but he could manage only ninth after serving his long-lap penalties from Balaton Park and now trails Bezzecchi by eight points.