The unseeded Indian overcame Nguyen 12-21, 22-20, 21-14 in a marathon match of one hour and nine minutes. This was Kashyap's fourth win over the Vietnamese in seven meetings. He had last beaten Nguyen in the group stages of the London Olympics in July.
In the first game, the World No.11 Vietnamese completely dominated play taking the lead from the first point, never giving it away at the Yuan Shen Gymnasium.
The second one was a topsy-turvy game with both exchanging serves at regular intervals. At one point, Kashyap took a lead of 15-10 but the seventh seed came back to equalise at 17-all.
Down at 19-20, the Hyderabadi not only saved the critical match-point but also took the next two points to seal the game.
The third game saw a neck-and-neck fight at the start. But from 8-all, the World No.23 Indian took a lead and never looked back, sealing the game with a gap of seven points.
The London Olympics quarterfinalist will next face World No.17 Chinese Wang Zhengming Friday for the first time ever to book a place in the last four.