The 20-year-old Bansod beat the junior world No 1 Tasnim Mir 21-13, 21-15 in a 33 minute clash. She will next face 18-year-old Tanya Hemanth on Friday.
Another pre-tournament favourite Ashmita also sailed into the quarter-finals after beating Anupama Upadhyaya 21-17, 21-16 in her round of 16 clash.
Both Malvika and Ashmita, with world rankings of 67 and 69, respectively, are the top-rated Indian women at the Super 100 event in the absence of Olympic medallists PV Sindhu and Saina Nehwal.
In the men's singles, third seed Subhankar Dey beat Rahul Yadav Chittaboina 21-16, 21-14. He will be facing Kiran George, who defeated Chirag Sen 21-12, 21-13, in the quarter-finals.
Another Indian contender in men's singles, Mithun Manjunath, also registered a 21-11, 21-18 win over Malaysian seventh seed Cheam June Wei. Manjunath is set to face a stiff challenge against the winner of last year's Ukraine International Priyanshu Rajawat on Friday.
In the mixed doubles, MR Arjun and Treesa Jolly moved into the quarter-finals with a straightforward 21-18, 21-5 victory over Raju Mohamed Rehan and Jamaludeen Anees Kowsar.
The winning pair will face Nazeer Khan Abu Bakkar and Nila Valluvan in the next match.