Jaisha clocked a timing of 2:47.19 hours, while Kavita clocked 2:59.29.
The event was dominated by Jemima Jelagat Sumgong, 31, of Kenya who clocked 2:24.04 to win the gold medal, followed by Bahrain's Eunice Jepkirui Kirwa who clocked 2:24.13 and clinched the silver medal.
Ethiopia's World champion Mare Dibaba won the bronze medal clocking 2:24:30.
The three medallists stayed together until the final 2 km when Dibaba dropped off the pace in the warm conditions, reports Xinhua.
Sumgong then pulled away from Kenya-born Kirwa in the final kilometre.
"I was never worried that I'd lose this," said Sumgong. "At 40 km I knew the gold was mine. At 35 km I noticed that my other two team-mates had dropped off and that gave me the motivation to carry on.
"At 40 km I saw there were three of us but I knew whatever happened I couldn't lose the gold and then I knew I was on the way to history."
Ethiopia's Tigist Tufa, who was favourite to win the race, pulled out before the halfway point.
It was Kenya's first victory in the Olympic women's marathon following three straight silver medals. It was also Kenya's first yellow metal at the Rio Games.
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