Bagnaia looked on course to take the sprint victory on Saturday when he crashed out of the lead on the final lap.
Biding his time in the first half of the race, Bagnaia reeled in Pramac’s Martin to overhaul him on lap 19 of 24, before streaking away by 1.740 seconds to score his third grand prix win of the season.
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It moves him back up to second in the standings, though Martin has still extended his advantage to 39 points after finishing second in the grand prix.
Marquez was one of four riders to gamble with the soft rear tyre in the sweltering conditions and used it to come from 14th on the grid to take third by just 0.052s from Aprilia’s Aleix Espargaro.
Ducati’s Bagnaia grabbed the holeshot from second on the grid from Tech3 GasGas rider Pedro Acosta, KTM’s Brad Binder, Martin and poleman Espargaro.
Acosta, also on the soft rear — along with Jack Miller (KTM), who crashed, and Alex Marquez – launched an attack on Bagnaia’s lead at Turn 10 on the third tour but ran wide and let the Ducati back into the lead.
Miller would crash just seconds later behind the leaders at the same corner, while Martin passed Acosta there for second on the following lap.
Martin then passed Bagnaia at Turn 10 on lap five to take the lead, with Acosta following the Pramac rider through on the sixth tour.
The top two quickly opened up a gap of over a second to Bagnaia, with Martin released into a 1.1s lead when Acosta crashed on lap 11 at Turn 10.
Bagnaia steadily chipped into Martin’s lead over the next few laps, getting it down to seventh tenths at the start of lap 16.
Martin’s lead fell further until Bagnaia lined up a successful attack into Turn 5 – where he crashed in the sprint on Saturday – on lap 19.
Bagnaia eased away from Martin to secure an important victory after his sprint woes, with Martin second.
Marquez’s charge from 14th started with a jump up to 10th on the opening lap, but found himself stuck behind Pramac’s Franco Morbidelli until lap 11.
Once free of Morbidelli, Marquez quickly passed a struggling Binder on lap 12 and got up to fourth ahead of Trackhouse Racing’s Raul Fernandez six tours later.
Espargaro – who won the sprint on Saturday 48 hours after announcing his retirement from MotoGP – couldn’t keep Marquez at bay and fell to his advances on lap 21 at Turn 1.
The Aprilia rider piled the pressure on Gresini’s Marquez over the final lap, but came up just 0.052s short.
Fabio Di Giannantonio was fifth on his VR46 Ducati, with Raul Fernandez sixth ahead of Alex Marquez (Gresini) and Binder. Yamaha’s Fabio Quartararo was ninth, with Miguel Oliveira (Trackhouse Racing) 10th.
The final points went to Marco Bezzecchi (VR46), Maverick Vinales (Aprilia), Acosta following his crash, LCR Honda’s Takaaki Nakagami and factory Honda counterpart Joan Mir.
Enea Bastianini crossed the finish line in ninth, but was handed a 32-second time penalty for failing to comply with two long lap penalties and a subsequent ride-through for ignoring his earlier punishments.
This dropped the factory Ducati rider down to 18th.
Tech3’s Augusto Fernandez and Morbidelli joined Miller on the sidelines after crashes at Turn 10.