This was Tipsarevic's first match of the tournament after receiving a bye past the opening round. He has lost his opening match in seven events this year, but he also won a tournament in India at the start of the season.
He defeated Bemelmans 6-4, 7-5, setting up a quarterfinal match with Alejandro Falla.
Falla eliminated Matthew Ebden 7-6 (7-1), 6-1 after surprising Xavier Malisse in the opening round.
The other second-round matches contested Thursday saw Matteo Viola upset fourth-seeded Edouard Roger-Vasselin 6-3, 7-5 and Vasek Pospisil defeat James Duckworth 7-5, 3-6, 7-5.
Viola and Pospisil will meet in the quarterfinals. The other quarterfinal matches, which were determined Wednesday, will find Adrian Mannarino taking on Ivo Karlovic and Santiago Giraldo facing No. 2 seed Kevin Anderson.