Bombayla won 27-24, 27-24, 26-27, 28-26 at the Sambodromo.
Earlier, she defeated Austria's Laurence Baldauff 105-98 in the 1/32 Eliminations Women's Individual round match.
Bombayla started the match with 9 pointer, following it up with a seven and an eight.
But the cumulative 24 points in the first set were not enough for her to win as Laurence scored three consecutive nine's to take a three-point lead.
But Bombayla quickly found her rhythm to score 28 in the second round to win 28-24.
She maintained the momentum in the third set with three straight nine pointers, forcing her Austrian opponent to concede the second set 27-23.
The 31-year-old Manipuri completed her victory in the fourth set with a 28-26 margin.
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