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A lopsided home win over the 'Squirrels' saw Kawasaki pip Kashima Antlers on goal difference after the defending champions were held to a scoreless draw at Jubilo Iwata.
Kobayashi smashed in a treble after Hiroyuki Abe's early goal, before Tatsuya Hasegawa added a fifth with the last kick of the game.
The final whistle sparked jubilant scenes from the Kawasaki players and home fans as Frontale completed a remarkable late charge to their first ever J-League title.
"It was a difficult season and we've gone through some turmoil," said a tearful Kawasaki manager Toru Oniki, whose side were beaten in the J-League Cup final last month.
"But all the frustration disappeared today."
Kawasaki, an industrial city sandwiched between Tokyo and Yokohama to the south, suffered more heartbreak in September when they were dumped out of the Asian Champions League in the quarter-finals by eventual winners Urawa Reds.
"We were tired but after coming this far the fatigue we felt didn't matter," added Oniki.
"We just wanted to leave everything out there and credit to the players, they did that."
Kashima's bid for a record-extending ninth J-League title collapsed after two successive 0-0 draws.
"We're gutted," said Kashima defender Gen Shoji, who revealed that Brazilian great Zico, a former Antlers player, had visited the team over the summer to give them a pep talk.
"Zico told us that coming second means nothing. We were top up until the end but finally finished looking up at the view from below -- I feel deeply sorry for failing to carry out Zico's wishes. We just weren't good enough."
Kawasaki and Kashima finished on 72 points from 34 games but Frontale boasted a vastly superior goal difference.
"It feels amazing," said sharp-shooter Kobayashi, who finished as the J-League's top scorer with 23 goals.
"This makes all the low points worthwhile, but it's more about the team than individuals. I'm just happy my goals helped the team win the title."
