The 26-year-old delighted the huge home crowd by finishing third at his home grand prix, fending off a late challenge from the McLaren of Jenson Button to become just the third Japanese driver to finish on an F1 podium.
Takuma Sato had been the last to finish in the top three at Indianapolis in 2004, while Aguri Suzuki finished third in Japan in 1990.
Kobayashi had admitted earlier in the weekend he needed a big result from this race, with rumours that he may leave Sauber at the season's end as Esteban Gutierrez and Jaime Alguersuari are linked with seats at the Swiss team.
And he produced when it mattered, rounding off a strong weekend which had seen him start third and outshine team-mate Sergio Perez.
The McLaren-bound Mexican retired early in the race after botching an attempt to pass Lewis Hamilton, the man whose drive he will take next year.
When asked if the race would be enough for him to keep his drive, Kobayashi said: "I think so."
He added of his battle with Button: "I needed to push, I could not slow down to save tyres. Whatever I had, like oversteer, I had to really push.
"In the end, into the last lap, I was pretty sure I could hold Jenson because normally after the main straight there is no chance to overtake on this track.
"Apart from that I was focusing on every lap because if I missed one corner, we could easily have lost my position so I think it was a good challenge for myself and I think Jenson was pretty fast in the last stint.
"Finally, we survived and let's say it was a great job from the team, because they gave us great advice while I was driving, and I was pretty sure to hold him and I was very happy. Every fan was waving their hands at me, especially on the last lap so it was fantastic."
Sauber chief executive Monisha Kaltenborn would not say whether the result was enough to secure Kobayashi's seat, but was pleased for him after being overshadowed by the three podiums Perez has recorded this year.
She said: "For us it does not change much as it would not have been the other way around if he had not had a good result, we would not have said 'that is it because you couldn't do it, you are not going to be here next year.'"
"We are in the process of making our decision and we know him well, we know his strengths very well, so we don't need these kind of things.
"I think it is important for him to have this kind of result for his own standing and his own career because if you look at the facts he has had a tougher season (than Perez), and that is where you have to be careful when judging him as a driver.
"If you look at most of the podiums where we had them, he was the fastest qualifier, which meant he had restraints on the tyres and strategy, and with the other car you could simply take a risk and the risk worked out and paid off.
"You have to be careful when comparing our drivers, I think he has been very unlucky this year and it is high time he was not unlucky."