Fabio Fognini of Italy beat Tommy Haas for the second time in two weeks to also advance to the semifinals.
Fognini prevailed 6-2, 6-4 over the second-seeded home favorite. The 12th-seeded Italian is looking for his second straight title after winning his first tournament in Stuttgart, where he beat Haas in the quarterfinals.
Fognini next faces third-seeded Nicolas Almagro of Spain, who came from behind to beat defending champion Juan Monaco of Argentina 4-6, 6-0, 6-3.
The fifth-seeded Monaco beat Almagro in the Hamburg semifinals last year. Almagro was runner-up in Hamburg two years ago, while Monaco beat Haas for the title last year.
Delbonis' previous semifinal appearance was two years ago, also on clay and also in Germany, in Stuttgart.
After fending off a pair of match points in the second set, Delbonis failed to serve out the match at 5-3. He then wasted two match points on Verdasco's serve before the Spaniard double-faulted on the third.