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At the start of the race, Tomoki Nojiri pulled away cleanly from pole, with Kobayashi following closely behind in second position.
After an unsuccessful attempt on lap 11, Kobayashi went around the outside at Nojiri at turn 1, making the move stick to take over the lead.
A few laps later, James Rossiter and Katsumasa Chiyo crashed at the very same corner, with the safety car subsequently deployed leading to race-defining split strategies.
While Kobayashi and a handful of drivers stayed out, the majority of the field pitted over the next few laps, with Yamamoto the lead driver to have got his mandatory stop out of the way.
That left Kobayashi with a major disadvantage, but the KCMG put the hammer down as soon as the SC pulled in, building a mammoth 27-second advantage to Yamamoto before pitting on lap 44.
However, a slow rear-left tyre change meant that he returned on track in net fifth place - and then lost a position to Narain Karthikeyan on cold tyres.
Kobayashi’s botched stop allowed Pierre Gasly’s former Super Formula teammate Yamamoto to score back-to-back Super Formula wins, the Mugen driver crossing the chequered flag with a 9.424s lead in hand.
Former European F3 frontrunner Nick Cassidy scored his second Super Formula podium at a track he claimed pole last year, the Kiwi having stopped as early as lap 6 and spent the remainder of the race on the faster soft tyre.
Kazuki Nakajima finished less than a second behind in third, scoring his first podium finish since last year’s Sugo round.
2016 Formula V8 3.5 champion Tom Dillmann recovered from electrical problems in qualifying to finish fourth on his first Super Formula start, making 14 places from his grid position.
Karthikeyan secured his first Super Formula points since 2016 with a fifth place result, while a disappointed Kobayashi crossed the line in sixth, over 25 seconds behind race winner Yamamoto.
Polesitter Nojiri was classified two seconds up the road in seventh, while Kenta Yamashita occupied the final points-scoring position in eighth.
Ryo Hirakawa, who pitted a lap after the SC was deployed, and Honda junior Nobuharu Matsushita completed the top 10.
Meanwhile, Red Bull junior Daniel Ticktum shot from ninth to sixth on his Super Formula debut, but contact with Koudai Tsukakoshi on lap 14 left him with a suspected puncture.
Ticktum managed to safely reach the pits after briefly running wide, but he eventually had to retire from the race with suspension damage.
|14||Takuya Izawa||Nakajima/Honda||1 Lap|
|15||Kazuya Oshima||LeMans/Toyota||1 Lap|
|DNF||Yuji Kunimoto||Inging/Toyota||22 laps|
|DNF||Katsumasa Chiyo||B-Max/Honda||53 laps|
|DNF||James Rossiter||TOM'S/Toyota||53 laps|
|DNF||Daniel Ticktum||Mugen/Honda||54 laps|
Sugo Super Formula: Nojiri beats Kobayashi to pole
New Super Formula car completes first running