Kobayashi, who now looks set to stay on in the Japanese series next year after hinting at an exit previously, posted a time of 1m36.296s in his Toyota-powered KCMG SF23 on Thursday afternoon to end the three-day test on top.
The Le Mans 24 Hours lap record holder had an inauspicious start to the day when he crashed at the final corner and brought out an early red flag, but was able to return to the track later and set a time that was seven tenths quicker than the lap with which TOM'S driver Sho Tsuboi had topped the opening day's running.
Nearly all of the fastest times from the test were set in the fourth session on Thursday as the track's grip was at its best and drivers experimented with low-fuel short runs.
Kobayashi's team-mate Nirei Fukuzumi made it a 1-2 for KCMG at the top of the combined order, lapping the Suzuka circuit in 1m36.337s to end up just 0.059s behind his countryman.
Fukuzumi, who is ending a decade-long relationship with Honda in favour of a move to rival Toyota, is vying for the second seat at the Hong Kong-based squad alongside Impul outcast Yuhi Sekiguchi.
Seven-time Super Formula race winner Sekiguchi drove for KCMG on the opening day and set a time of 1m37.027s in the morning session, which put him second at the end of the day's running but well outside the top 10 in the overall order.
Third place in the combined standings went to day one pacesetter Tsuboi, the newly-crowned SUPER GT champion, after he improved by six tenths on Thursday to set a best time of 1m36.363s.
Tsuboi is expected to replace reigning Super Formula champion and his GT500 team-mate Ritomo Miyata at Toyota powerhouse TOM'S next year following the 24-year-old's move to Formula 2 with Rodin Carlin.
Red Bull/Honda junior Ayumu Iwasa ended up fourth in the order, just 0.024s behind Tsuboi, as the top Honda driver in the standings.
Being a complete newcomer to Super Formula, Iwasa was able to get three days of track action in the Mugen SF23, including on the final day of running reserved for rookies.
Iwasa's quickest time came on Friday morning, having been unable to set a time in the 1m36s bracket on Thursday afternoon when most of his rivals focused on short runs.
Behind Iwasa, Kenta Yamashita finished a strong fifth for Kondo Racing with a time of 1m36.392s, just edging out Toshiki Oyu in the lead Inging car.
Oyu is leaving Honda after a trying dual campaign in both Super Formula and SUPER GT with the Sakura-based manufacturer.
Source: Autosport