At the wheel of the #23 Nissan Z, Quintarelli scored his and Matsuda's first pole since the 2019 Fuji round, and also became the first non-Toyota polesitter of the 2022 season.
The Italian took the top spot with a best time of 1m45.169s at the end of the Q2 pole shootout to beat the #17 Real Racing Honda NSX-GT of Nobuharu Matsushita by 0.180s.
Honda had topped Q1 courtesy of the Mugen car of Toshiki Oyu, but team-mate Ukyo Sasahara couldn't quite match Oyu's pace in Q2 and ended up third-fastest on a 1m45.442s.
The Racing Project Bandoh Toyota GR Supra that had been on pole for the last three races was only fourth in the hands of Yuji Kunimoto, followed by the Cerumo Toyota of Yuji Tachikawa.
Kohei Hirate was sixth in the Kondo Nissan Z, while the Q2 order was completed by the SARD Toyota of Yuichi Nakayama and Tadasuke Makino aboard the Team Kunimitsu Honda.
None of the three cars carrying stage one fuel flow restrictors made it out of the opening phase of qualifying.
Katsumasa Chiyo came closest to doing so in the #3 NDDP Racing Nissan that won at Suzuka in May, but had to settle for ninth, while Ritomo Miyata was 11th aboard the points-leading TOM'S Toyota and Kenta Yamashita ended up down in 14th place in his Rookie Racing Supra.
GT300: Gainer on top, Subaru struggles
Pole in the GT300 class went to the #10 Gainer Nissan GT-R NISMO GT3 of Ryuchiro Tomita and Riki Okusa.
Okusa had taken pole for Super GT's previous visit to Suzuka in May, only to fail post-qualifying technical inspection, and the rookie was the man to beat again this time around, posting a 1m56.995s to beat the Max Racing Toyota GR Supra of Atsushi Miyake by 0.054s.
Takashi Kogure was third-fastest at the wheel of the #88 Lamborghini Huracan GT3 Evo in third, followed by the championship-leading Kondo Racing Nissan GT-R of Kiyoto Fujinami and Tatsuya Kataoka in the Goodsmile Racing Mercedes-AMG GT3 Evo.
The championship-leading Subaru, carrying 88kg of success ballast after its Fuji win, dropped out of Q1 and will start down in 22nd place, one place ahead of the Team Studie BMW M4 GT3.