The Chinese women had won the last seven of eight gold medals at the Asian Games in the 4x100m but had to be satisfied with silver after the Bahrain team won in a Games record 42.73 seconds. Kazakhstan picked up the bronze.
Japan won gold in the men's 4x100m relay in a time of 38.16 seconds with a team that included three of the four sprinters who came second at the 2016 Olympics.
"Very happy to win gold and hear the national anthem play as we missed it at the Olympics and the world championships," Japan's Aska Cambridge told reporters.
"We are aiming to average 37 seconds in Japan training consistently to win the gold at the Tokyo (Olympic) Games (in 2020)."
World junior 100m sprint champion Lalu Muhammad Zohri brought the crowd to their feet by helping the hosts win silver while China, with 100m Asian Games sprint champion Su Bingtian, could only manage bronze.
The 21-year-old Odiong had completed the women's sprint double with the 100m and 200m titles at the Gelora Bung Karno Stadium and also won silver in the 4x400m relay later on the final day of athletics at the 18th Asian Games.
"I thank God for giving me three gold medals," she said. "I am very happy and I am happy for my team mates, they did a marvellous job. I love you all."
Odiong was denied a clean sweep of golds in the 4x400m relay by India, who won a fifth straight title in the event.
Bahrain's Nigerian-born Salwa Naser, who won the 400m gold, also finished with four medals.
Bahrain ended another prosperous day on the track when they also managed one-twos in the women's 1500m and men's 5,000m. The country finished with 25 medals from athletics, with 12 gold, six silver and seven bronze.
China's Wei Yongli, who recently became the first Asian woman to break the 11-second barrier in 100m sprint, felt the African-born athletes in the Bahrain squad would only help raise the standard of the sport in Asia.
"We are unfamiliar with this team (Bahrain), we don't know them until today, although it is a pity we didn't win but we did our best," Wei told reporters after the 4x100m relay. "This is sports, there is no such thing like unfairness.
"I think it is good. With their presence they will bring the standard of Asian sports a tad higher and also help us to push ourselves to improve."
(Additional reporting by Angie Teo and Jessica Damiana; editing by Toby Davis)
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