The DAMS driver was lingering around the bottom of the top 10 before jumping up to fifth on his penultimate attempt.
But a stunning final flying lap from the Japanese driver shot him to the top spot, a 1m27.930s almost 0.4s clear of second-placed Marcus Armstrong (Hitech) and the only driver to dip below the 1m28s barrier.
Championship leader Felipe Drugovich will line up third for Sunday's feature race with MP Motorsport, with title rival Theo Pourchaire (ART) joining him on the second row.
Armstrong was first to set a flying lap, setting a benchmark of 1m29.228s to immediately better Jack Doohan's practice-topping time of 1m29.562s.
The Virtuosi driver slotted into second with his first flying lap, demoting Liam Lawson, Juri Vips and Logan Sargeant, who put in early efforts.
Pourchaire was next to claim the top spot, with a 1m28.883s, but was quickly toppled by teammate Frederik Vesti, who went 0.03s quicker.
Drugovich moved up to second on his second attempt, splitting the ARTs, while Sargeant, who sits third in the drivers' standings, sat in seventh, a 1m29.285s his best so far.
As the field pitted for new tyres around the halfway mark, Olli Caldwell set a sensational 1m28.803s to briefly claim the top spot having run in the gap.
Despite the Campos driver's stellar effort, he finished the session in 13th, bettering his previous personal best qualifying result of 16th.
Doohan and Prema Racing's Jehan Daruvala opted to hold back in the pits in a bid to avoid the traffic seen in FIA Formula 3 qualifying earlier in the day, while further ahead Armstrong reclaimed the top spot with a 1m28.311s, having been running sixth.
Sargeant went second on his next attempt, with a 1m28.381s, before Pourchaire demoted him to third having gone 0.02s quicker.
On the final flying laps, Vips jumped up to fourth with a 1m28.391s, while Drugovich improved to second as Pourchaire stayed third and Iwasa was running in fifth, with a 1m28.530s.
But the Japanese driver's final lap was the decider, putting him to the top of the timesheet with just two minutes remaining, and with those running behind him unable to improve.
Sargeant will line up fifth, with Vips and Vesti in sixth and seventh.
Doohan takes pole for Saturday's reverse-grid sprint race, with Enzo Fittipaldi and 2021 F3 champion Dennis Hauger lining up second and third.
F2 Hungary: Full qualifying result
