Giri overcame India junior No. 4 Vishal Vaya in the decider after enjoying a 2-0 advantage when Vaya forfeited the first two frames for arriving late for the Group G tie.
But Vaya fought back to snatch the third and fourth frames before a substantial lead gave Giri the edge in the fifth and final frame.
Later, Giri got past NSCI pre-quarterfinalist Rajvardhan Joshi of PYC Hindu Gymkhana, Pune, 3-1.
In the same group, Bangalore lad Arjun Mehta experienced mixed fortunes while overcoming Saigal 3-2 and going down to Shah 1-3.
Asian 6-Red snooker bronze medallist Laxman Rawat, Aashit Pandya of Dombivli Gymkhana, Chennai's Pranit Ramchandani, Nikhil Ghadge of Matunga Gymkhana, Rovin D'Souza of PJ Hindu Gymkhana and Aditya Agrawal of Indian Snooker Academy all won their second ties in as many outings to improve their chances of qualifying for the next stage.