However, the tournament was over for fourth seed Sameer Verma after he retired hurt against Ireland's Nhat Nguyen.
Bansod took just over half an hour to dispatch 16-year-old Tasnim in the pre-quarterfinals
Former world No. 1 Saina, who missed a lot of tournaments last year due to multiple injuries, moved to the second round after her opponent, Czech Republic's Tereza Svabikova, suffered a back injury and retired mid-way while trailing 20-22, 0-1 in an opening round match.
Indian shuttler Sourabh Varma reached the semi-finals of the Belgian International Challenge after an easy victory over Kieran Merrilees of Scotland in the men's singles competition in Leuven, Belgium, on Friday.
Commonwealth Games bronze medallists Ashwini Ponnappa and N Sikki Reddy scored a stunning straight games victory over world No. 18 Li Wenmei and Zheng Yu to make it to the second round in the women's doubles at the US $350,000 India Open, in Delhi, on Tuesday.
Still recovering from a foot injury and a recurring fever, defending champion Saina Nehwal has pulled out of the women's singles competition at the Syed Modi Grand Prix Gold badminton tournament in Lucknow.
Conor McGregor said on Tuesday he was retiring from the sport, five months after losing to Khabib Nurmagomedov in a controversial title fight
A summary of sports events and sports persons, who made news on Wednesday
Summary of sports events and persons who made news on Saturday
A summary of sports events and sports persons, who made news on Saturday.
A summary of sports events and persons who made news on Tuesday