Thailand's Intanon booked her place in the last eight with a 21-6 14-21 21-11 victory over China's Sun Yu in an evenly contested match that lasted all of 58 minutes.
Li had a far easier time of things, however, notching a 21–18 21-17 victory over another Thai player, Porntip Buranaprasertsuk.
Joining them in the last eight are third seed Tai Tzu Ying and fourth seed Wang Shixian, who recorded contrasting victories on Thursday.
Local player Tai made short work of her opponent on the day – PV Sindhu – winning 21-15 21-17 in just over half an hour, but Wang needed all of 76 minutes to overcome Sayaka Takahashi, eventually coming through 21-18 10-21 24-22.
Sixth seed Wang Yihan eased past Chochuwong Pornpawee 21-13 23-21, while eighth seed Nozomi Okuhara beat Nitchaon Jindapol 21-14 21-16.
In the other last 16 matches that were concluded on the day, Bae Yeon Ju beat Fitriani Fitriani 21-10 21-13 and Sayaka Sato trounced Kim Hyo Min 21-17 21-7.