Seppi, the No. 3 seed, defeated the eighth-seeded Granollers 6-4, 7-5. They were the only seeded players to make the quarterfinals.
Seppi dropped only nine points and faced one break point -- which he lost -- in 11 games serving. But he won the only break point of the second set in advancing.
His semifinal opponent will be Bernard Tomic, who survived the only three-set match in the quarterfinals, beating Jarkko Nieminen 6-7 (6-8), 6-4, 6-2. The seesaw first set saw two breaks by each player but Tomic allowed Nieminen just one break opportunity the rest of the way.
Also Thursday, Julien Benneteau defeated Ryan Harrison 6-4, 6-2 without facing a break point and winning 75 percent of the points on serve and Kevin Anderson topped Denis Istomin 6-4, 6-3 behind four breaks.
Anderson and Benneteau, who has a 2-0 series edge over Anderson, square off in one of Friday's semifinals. Tomic won the only previous time he played Seppi.