Pospisil had the only break of the match and that was worth the second set of a 7-6 (8-6), 6-4 win over Hewitt. Pospisil fired off 12 aces and saved all three break points he saw. He won more than 70 percent to the point son serve.
Qualifier Ruben Bemelmans posted a 6-2, 6-0 rout of Jan Hajek. One of the games he lost came on a break but he won 65 percent of the points serving and 61 percent off Hajek's serve.
He was one of three qualifiers to pull off wins Tuesday. Miloslav Mecir beat Pablo Andujar 6-4, 6-4 without facing a break point and Mirza Basic topped Michael Russell 6-6-3, 6-4 by fighting off all 13 break chances Russell managed.
Daniel Brands defeated Andreas Haider-Maurer 6-4, 7-6 (7-5) and earned shot at top-seeded Jo-Wilfried Tsonga. Also Tuesday, Dominic Thiem beat Daniel Gimeno-Traver 6-4, 5-7, 6-4; Robin Haase came out a 5-7, 6-2, 6-2 winner over Ilija Bozoljac and Lukas Lacko ousted Gerald Melzer 7-6 (7-5), 6-1.