Bagnaia recorded just his second win of the season as he held on on his factory Ducati despite poleman Marquez's gargantuan efforts on his Ducati satellite Gresini bike.
Marquez, whose last pole position was the Portuguese MotoGP in March, 2023, has had several years of fitness and injury problems.
However, the 31-year-old six-time former MotoGP champion laid down a marker that he is back as he recorded his best finish since being runner-up in the Australian MotoGP in October, 2022.
Marco Bezzecchi took third -- his first podium of the season -- whilst championship leader Jorge Martin crashed out when leading with 15 laps to go.
Martin, who won Saturday's crash-filled sprint race, retains his lead in the standings, 17 points ahead of Bagnaia.
Despite some bad blood between Marquez and Bagnaia they managed a genuine enough looking hug after they had ridden into the pits following celebratory laps.
Marquez held his lead going into the first corner with Martin in second.
However, it was Bagnaia who took the eye surging from seventh to overtake Marquez going into the second lap, the record crowd having cheered as the Spanish great led into the straight.
Martin then assumed the lead as he and Marquez passed Bagnaia in the straight at the end of the second lap -- but Bagnaia battled back to overtake Marquez.
Marquez slipped to fourth as Bezzecchi passed him.
Martin and Bagnaia pulled away from Bezzecchi and Marquez.
The race changed dramatically at the Dani Pedrosa corner with 15 laps remaining as perhaps unnerved by Bagnaia's pressure Martin made an error and slid off.
This left Bagnaia -- whose only win and podium has come in Qatar this year -- nearly a second ahead of Bezzecchi and Marquez.
Bezzecchi appeared to be in trouble, sliding all over the track and Marquez eased past him sparking the packed strands to erupt in joy.
Marquez had the bit between his teeth and began eating into the Italian's lead.
'Angry exchange'
However, Bagnaia showing the steeliness that has brought him two successive titles hit back posting a fastest lap.
Nevertheless Marquez was not beaten and closed right up on Bagnaia posting a record lap time with five laps remaining.
Marquez actually had the lead briefly as he went past Bagnaia but the Italian somehow managed to regain it immediately.
No quarter was expected as there is no love lost between the two of them heightened after an angry exchange at this season's Portuguese MotoGP when Bagnaia was seething after crashing in a collision with Marquez.
Bagnaia eased some of the pressure with a fastest lap three laps from the chequered flag and despite the ear-splitting roars from the packed stands -- a record 296,000 attended the circuit this weekend -- the 27-year-old held his nerve.
Marquez has not won a race since securing his 59th career win at the Emilia-Romagna Grand Prix in October 2021 -- 900 days ago.
There was none of the carnage from the sprint race, but nevertheless several failed to finish.
Veteran Dani Pedrosa's race ended early, the 38-year-old had moved up to 11th but soon afterwards his day's work was over.
A collision between Johann Zarco and Aleix Espargaro ended their races with 16 laps to go, the latter shaking his fists in frustration at his second crash in two days.
There were more fists being shaken with eight laps remaining as Jack Miller was furious at Franco Morbidelli, who came in on him as he tried to pass him on a corner.
Race officials had to step in to prevent the irate Australian having a go at the Italian.
The riders take their show next to the French MotoGP in Le Mans in a fortnight.
