Bagnaia edged out his teammate with a time of one minute 29.634 seconds in Q2, denying Marquez what seemed like a certain pole after the Spaniard had set the benchmark earlier in the session.
"I hope (things are starting to click), it's never easy to say it after what was happening last year," Bagnaia said.
"So keep calm, feet on the ground and work like we are doing... We found something (in the setup) that is helping me, so we just need to continue like this and try to maintain the same level."
Marquez's route to the front row was anything but straightforward after he failed to move directly into Q2 on Friday.
The Spaniard was forced through the Q1 qualifying session in which he initially found himself pushed out of the top two and in danger of missing final qualifying altogether.
But the Ducati rider's response was emphatic as he produced a scorching lap that shattered the circuit's lap record with a time of one minute 29.288 seconds.
The effort was so blistering that Ducati team manager Davide Tardozzi shook his hand like he had touched something hot in the garage.
"I'm in a moment that I don't understand many things, I need to understand the way I'm riding because it's true that I cannot be consistent," Marquez said.
"But when I have this extra adrenaline, I can do it because I know how to be fast on a bike."
Marquez and home favourite Fabio Quartararo advanced from Q1 to Q2, where the Spaniard once again looked to have done enough before Bagnaia's late intervention to claim his first pole of the season.
The Ducati duo will be eager to convert their front-row lockout into race success after both riders dominated the sprint in Jerez two weeks ago but failed to finish Sunday's race, won by Marquez's brother Alex.
Aprilia's championship leader, Marco Bezzecchi, joins the two Ducatis on the front row in third, while VR46 Racing's Fabio Di Giannantonio claimed fourth. KTM's Pedro Acosta and Yamaha's Quartararo complete the second row.
