Seppi got by Guillaume Rufin 1-6, 7-6 (7-5), 6-4 in a first-round match of the BRD Nastase Tiriac Trophy tennis tournament. The match took nearly 2 1/2 hours.
Seppi lost his serve four times but held serve through the third set while getting his third break of the day to advance.
Qualifier Daniel Brands took out Dodig 7-6 (7-4), 6-2. Dodig saved all three of the break points he faced and ended up winning 74 percent of the points on serve.
Fabio Fognini cashed in all three of his break-point opportunities in claiming a 7-5, 7-6 (7-5) decision over Joao Souza and Jurgen Zopp eliminated local favorites Victor Crivoi 6-3, 6-3, fighting off three break points.
Other first-round matches Tuesday saw Dudi Sela defeated Adrian Ungur 7-6 (7-2), 6-2 and Cedrik-Marcel Stebe advanced over Erik Chvojka 6-3, 6-3.