Bagnaia set a time of 1m44.855s with just under three minutes to go in Q2, edging out Marquez - who was following him on track - by just under a tenth of a second.
Amid a threat of rain in the second part of qualifying, all riders headed out on track early to get a banker lap in. After the first set of runs, it was Jorge Martin who led the session for Pramac on a 1m45.268s, with VR46's Marco Bezzecchi making it a 1-2 for Ducati at the front of the grid.
When the second set of runs began, Bagnaia encountered Marquez as he headed out of the pitlane, with the Italian rider visibly furious at his Honda rival for their run-in.
Bagnaia was able to move ahead of Marquez and then proceeded to begin his flying lap, but had to deal with the Spaniard following closely behind and taking advantage of his tow.
With rapid times in each of the four sectors, Bagnaia became the first rider to break the 1m45s barrier, moving to the top of the timesheets with two minutes and 50 seconds left on the clock.
Marquez appeared to be on course to better Bagnaia's time but wasn't able to match the final sector of the reigning champion, and had to settle for second with a time of 1m44.933s.
Marc Marquez, Repsol Honda Team
Photo by: Gold and Goose / Motorsport Images
No other rider was able to match the leading duo in the dying minutes of the session, with Bagnaia securing his third pole position of the season and Marquez clinching his third front-row start in as many attempts in 2023.
Marquez's younger brother Alex came all the way from Q1 to qualify third on the grid on his Gresini Ducati, setting a late time of 1m45.007s.
That left KTM's Jack Miller, who had also come from Q1, in fourth place, with Martin and Bezzecchi ending up fifth and sixth after failing to improve their times from their first runs.
A heroic effort from an injured Aleix Espargaro put him seventh on the grid on the factory Aprilia, ahead of the second Pramac Ducati of Johann Zarco and the LCR Honda of Alex Rins.
KTM's Brad Binder suffered a crash at Turn 11 in qualifying after setting a best time of 1m45.731s, which put him 10th on the grid ahead of Luca Marini (VR46) and Enea Bastianini (Ducati).
Bastianini, making his comeback after a long injury-induced absence, fell off his bike just three minutes into qualifying and had to rush to the garage to hop on his replacement chassis.
Maverick Vinales qualified 13th on the Aprilia after failing to progress to Q2 by 0.032s.
Both factory Yamahas also got eliminated in Q1, with Franco Morbidelli qualifying 14th ahead of team-mate and 2021 champion Fabio Quartararo. It was Quartararo's third successive Q1 elimination of 2023.
RNF Aprilia's Raul Fernandez suffered a big crash at Biondetti 1 with just a few minutes to go in Q1, leaving him 20th on the grid.