The London Olympics bronze medallist notched up an easy 21-12, 21-7 victory over Gilmour in a women's singles match that lasted only 30 minutes.
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 the men's singles.
Guru will next play third seed Chinese Pengyu Du in the last eight.
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.
India's top men shuttler Parupalli Kashyap also could not get across the world number five Jan Jorgensen of Denmark and suffered a 11-21, 15-21 defeat to the local star in a 35-minute match.
Outclassed most part of the match, Kashyap saved four match points in the dying moment but it was too little and too late in the end.
In the first game, Kashyap did put up a fight initially and was lagging 6-7 at once stage but Jorgensen didn't allow the Indian to get across him as he slowly and steadily moved ahead and then 15-11, reeled off six points to march ahead.
In the second game, Jorgensen enjoyed a 8-2 lead early on and though the Indian made it 6-8, the Dane never let it to threaten his game as he kept extending the gap and finally earned a massive match point, reaching 20-11.
Kashyap reeled off four straight points but eventually Jorgensen had the last laugh.
Image: Saina Nehwal
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