The World number five Indian rode on her smashes to see off Lan 21-17 21-13 in a 42-minute women's singles match at the CU Sport Complex.
The 22-year-old from Hyderabad will next take on the winner of the match between Japan's Kaori Imabeppu and eighth seed Sapsiree Taerattanachai of Thailand.
Top seed Saina took time to get off the mark and was forced to do the catch-up act most of the time during the first game.
The Indian levelled the score at 12-12 and waged a grim battle till 17-17, before reeling off four straight points to pocket the first game and lead the match 1-0.
In the second game too, Lan put up a fight in the initial moments but Saina was too good for her as she widened the gap from 7-7 to eventually seal the issue comfortably.
The other Indian in the women's singles competition, P V Sindhu, however, lost to former World Champion Wang Lin 12-21 23-25 in 36 minutes.
In the men's doubles competition, Sanjeeth S and Jagadish Yadav lost 12-21 6-21 to Calvin Jia Hong Ong and Wee Gleen Tan of Malaysia.
Another Indian pair of Tarun Kona and Arun Vishnu also bowed out with a 22-24 13-21 defeat to sixth seeds Ricky Karanda Suwardi and Muhammad Ulinnuha of Indonesia.
India's women's doubles pair of Pradnya Gadre and Prajakta Sawant also crashed out with a 19-21 12-21 defeat to the Malaysian combo of Amelia Alicia Anscelly and Fie Cho Soong in a 27-minute match.
Up against the top seeds Xia Huan and Jinhua Tang of China, the Indian pair of Aparna Balan and Siki Reddy N lost 10-21 13-21 in 24 minutes.
