Haas, seeded third, defeated Ernests Gulbis 7-6 (7-5), 6-4 without facing a break point. Gulbis pounded out 15 aces but also had seven double faults. Haas converted just one of his 17 break opportunities but that was the difference in the second set.
Haas dropped only 13 points over 11 games serving.
No. 1-seeded Roger Federer takes on Mischa Zverev while Haas meets Gael Monfils in Friday's quarterfinals from the top half of the draw. The other quarters send Gasquet against Florian Mayer and Kohlschreiber against Mikhail Youzhny.