The 27-year-old came from behind in the deciding game to beat Singapore's Derek Wong 21-14 11-21 21-19 and become the first Indian man to win badminton gold at the Games for 32 years.
"In this kind of big game to win gold is a big deal for me," Kashyap told reporters after coming back from 11-8 down in the decider.
"It's like a dream that I haven't dreamt of since I was a child."
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After taking the first game, the Indian shuttler admitted to under-estimating his opponent.
"I was becoming too tense. In my mind I believed I could win easily because I didn't think he could play such a good game so I wasn't ready because in my mind I had already won," Kashyap added.
Earlier, Canada's Michelle Li beat Kirsty Gilmour, the first Scottish woman to reach a singles final at the Games, 21-14 21-7 to win gold.
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