Seppi defeated Ivan Dodig 6-4, 6-2 behind five breaks. He won more points -- 33-30 -- off Dodig's serve than Dodig managed.
Fourth-seeded David Nalbandian also advanced in straight sets, taking care of Aljaz Bedene 6-4, 6-3. He won 70 percent of the points on serve, losing just six points over five games in the first set.
Gilles Muller, the No. 8 seed, will go against Seppi in the next round after Muller topped Eduardo Schwank 6-3, 7-6 (7-0).
Wednesday's other match saw Joao Souza move into the quarterfinals when Dusan Lajovic retired with Souza up 4-2 in the first set.