The London Olympics bronze medallist notched up a 21-12 21-7 victory over Gilmour in a women's singles match that lasted only 30 minutes here.
The world No 4 Indian will next take on the winner of sixth seed Korean Ji Hyun Sung and Tsz Ka Chan of Hong Kong.
Earlier, in a clash between two Indians, RMV Gurusaidutt enjoyed the bragging rights when he prevailed over Ajay Jayaram 21-15 21-16 in a men's singles match which lasted for 35 minutes.
In rampaging form during the Indian Badminton League, Saina took some time to get off the groove which allowed Gilmour to get into a slender 6-3 lead against the Indian in the early stages of the first game.
However, the Hyderabadi reeled off six straight points to zoom ahead to 9-6 and then didn't lower her guard again as Gilmour was left to do the catching up job.
In the second game, Saina surged ahead to a 6-0 lead but Gilmour managed to reduce the margin to 4-9. The Indian then extended the gap to a 13-4 lead and kept moving ahead, before eventually sealing the match comfortably.