Tipsarevic easily got by Edouard Roger-Vasselin 6-2, 6-3 without facing a break point and finishing off four of his own five break opportunities. Tipsarevic won 80 percent of the points on serve while dropping only eight points over eight games serving.
Also advancing with wins Wednesday were fourth-seeded Stanislas Wawrinka, No. 8-seeded Go Soeda and Aljaz Bedene, who pulled off the day's upset.
They are all in the bottom half of the draw and Tipsarevic will go against Soeda while Wawrinka plays Bedene in the quarterfinals.
Bedene defeated sixth-seeded Robin Haase 7-5, 6-3 while losing only 12 points in 11 games. He did have his serve broken once in the first set but won 20-of-23 points on serve in the second.
Wawrinka wrapped up Wednesday's singles schedule with a 6-4, 6-3 win over Cedrik-Marcel Stebe. Like Tipsarevic, Wawrinka didn't face a break point. He won the first set with a 10th-game break and went ahead in the second with a break in the second game.
Soeda got by the 551st-ranked Prakash Amritraj -- the son of Indian tennis great Vijay Amritraj -- 7-6 (7-2) 3-6, 6-4. Soeda fought off 14 of the 17 break points he faced to advance.