Italian Nadia Battocletti earned sweet redemption after just missing the podium in the 5,000m, taking silver in 30:43.35, and Dutchwoman Sifan Hassan failed to defend her Tokyo crown as she finished third in 30:44.12.
World record holder Chebet did her share of the early pace-making and when the pack broke into a sprint with one lap remaining she pulled away on the final turn to deliver Kenya's first gold medal in the event.
"To do the 5,000m and 10,000m is not something easy. But just focus, and know that you can achieve," she told reporters.
"Just believe in yourself. I believed that I can do it."
Battocletti, who finished third in the 5,000m but had her bronze medal taken away when Kenyan Faith Kipyegon's disqualification was overturned, made sure of her podium spot in the longer race.
Eritrea's Rahel Daniel, the leader through the first two laps, dropped out after 2,000 metres as Chebet stayed near the front of the pack at a comfortable pace.
Her compatriots Margaret Kipkemboi and Lilian Rengeruk joined her about two-thirds of the way through, as Hassan tried her usual strategy of hanging around near the back of the pack.
Hassan made her move with 400 metres to go as the leaders broke into an all-out sprint and Kipkemboi and Rengeruk lost ground as Battocletti moved past them.
Chebet ran down the final straight on her own and looked up at the results with sheer joy on her face before wrapping herself in the Kenyan flag.
She told reporters she prepared for the longer distance by completely putting the 5,000m gold out of her mind.
"Just focus and mind switch," she said.
"My country is watching me, so I have to focus on the 10,000m and not think that I've won a gold medal. That was my target."
Hassan still has the marathon left in her gruelling Paris programme and will have less than two days to recover before tackling a hilly and challenging course.
"Endurance on Sunday, that’s not a joke. To finish the marathon is a kind of hell. It’s not easy," she told reporters. "The real one will start Sunday."
