Mayookha controlled the long jump competition from the very outset and finished on top of the podium with a leap of 6.35m, an effort that propelled her to India's first Asian indoor title in the event.
Bui Thi Thu Thao of Vietnam took the silver with a 6.30m jump while Olga Rypakova of Kazakhstan finished third with an effort of 6.22m.
"Winning in Doha made me really happy, especially since I'm not used to competing indoors. However, I expected something better than 6.35m. But I'm not complaining at all. The Asian title is quite an achievement," said Mayookha after winning the gold.
Dutee, meanwhile, won a bronze in women's 60m dash with a time of 7.37 secs in the final. Earlier, she had set a national record while winning her heats in 7.28 secs.
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Viktoriya Zyabkina of Kazakhstan overcame a sluggish start to win the final race in a Championship record of 7.27 secs, well clear of China's Yuan Qiqi (7.33 secs).
Sugandha Kumari brought the third medal for India as she won a bronze in women's 1500m with a time of 4:29.06.
In women's shot put, Manpreet Kaur (Jr) finished sixth with her best throw of 15.21m. In men's high jump, Tejaswin Shankar failed to clear the opening height.