Bagnaia put on a brilliant final lap at the Sepang International Circuit to secure his first pole since the Catalan Grand Prix in September and beat last year's Malaysia poleman Martin, who crashed in the final minutes of the second qualifying session (Q2).
The Italian, chasing his second world crown, will be joined by Martin and Enea Bastianini of Ducati on the front row on Sunday as he looks to increase the gap to title-rival Martin, who trails by 13 points in the standings.
"It's one of the most important," Bagnaia said when asked how this pole position rated in his career. "Most of the lap times were incredible.
"I'm very happy. Being back in pole position is fantastic and it's going to be very positive for us this afternoon," he said, referring to the sprint race.
Martin looked on course to grab his fourth pole of the season and carry his flawless form from last month's Thailand Grand Prix until the Spaniard's dramatic crash at turn four, after which his provisional pole time of 1:57.549 was not enough.
"I feel good. We have to understand why the crash and don't repeat it in the race," Martin said.
Gresini's Alex Marquez will start fourth after showing promising pace throughout qualifying.
VR46 Racing duo Luca Marini and Marco Bezzecchi, third in the title race, took the fifth and sixth slots, respectively.
Brad Binder of KTM, Yamaha's Fabio Quartararo and Maverick Vinales of Aprilia were the other riders in the top nine.
Marc Marquez's qualifying ended painfully after the six-time MotoGP champion crashed in Q1 and will only start 20th on Sunday. His Spanish compatriot Aleix Espargaro, who sits fifth in the championship, also missed on a Q2 spot.
