The second-seeded Seppi advanced after Horacio Zeballos retired while trailing 6-5 in the first set. The Argentine had two set points at 5-4.
Seppi will next face fifth-seeded Tommy Robredo of Spain, who needed five match points to beat Slovenia's Aljaz Bedene 6-1, 6-4. Robredo has lost only 13 games in three matches so far in Umag.
Fognini, seeded third, beat Martin Klizan of Slovakia 6-4, 6-2 for his 12th consecutive singles victory to reach his third semifinal at Umag. Fognini won four consecutive games after trailing 3-1 in the first set. Another four-game run in the second at 1-1 set up the victory.
''I played much better than on the first day, I felt great,'' Fognini said. ''My game really works good at the moment. Still, the top 10 is not my goal now, it is a long road. I just entered the top 20.''
Fognini will face Gael Monfils of France, who needed 2 hours, 16 minutes to defeat Spain's Albert Montanes 6-2, 5-7, 7-5. Monfils had a chance to finish the match in straight sets when leading 5-3 in the second set, but he lost four games in a row.
''I got a bit tight when I served for the match at 5-4 in the second set. I should have been more aggressive,'' Monfils said. ''I am very pleased with this. I've never beaten Albert on clay before. It was good clay-court match. I could have served better and surely it might be improved tomorrow.''