TOM'S driver Cassidy finished third from 10th on the grid, leading for much of the latter half of the race as he left his mandatory pitstop until the penultimate lap.
The New Zealander was locked in a virtual battle with Inging driver Sho Tsuboi, who chose to stop early and was then able to pass teammate Hiroaki Ishiura for the net lead.
Podium: Sho Tsuboi, Inging, Hiroaki Ishiura, Inging, Nick Cassidy, TOM'S
Tsuboi meanwhile was able to celebrate a first-ever Super Formula victory in only his ninth start in the category, an unlikely turnaround after he crashed at the end of qualifying.
That incident left him eighth on the grid, but a good start combined with a three-way collision at Turn 1 involving Sacha Fenestraz, Tadasuke Makino and Oyu left him second at the end of the first lap, only behind poleman Ryo Hirakawa.
Tsuboi pitted on lap 11, one lap before Hirakawa, and managed to pass the Impul driver with the help of his warmer tyres - repeating the trick on Ishiura almost 20 laps later.
"I knew that if I could do a good lap in qualifying, I could start from the top," said Tsuboi, who failed to complete a lap of the season-opening Motegi race.
"That's why I was so disappointed after I crashed, my heart was in tatters. I knew I was in good shape and I just wanted to focus on finishing the race, to feel the car without rushing, and hoping for a better result in the next one.
"But after turn one I knew I had a chance to win and I'm glad to have seized it."
He added: "I knew the pace would be good for the first few laps after the safety car [deployed in response to the first-lap incident], and I thought it might be possible to jump Hirakawa.
"I was watching Hirakawa and he didn't come in on lap 11, so I came in, and that strategy worked well. The tyre change was quick, which I think was key to passing."