Federer beaten by world number 114 in Hamburg
The former world number one went down 7-6 (9/7), 7-6 (7/4) to the 22-year-old Delbonis with the defeat coming just a month after Federer was knocked out of Wimbledon by Ukraine's world number 116 Sergiy Stakhovsky in the second round.
Delbonis will play Fabio Fognini in Sunday's final after the Italian 12th seed reached his second successive final by beating Spain's Nicolas Almagro 6-4, 7-6 (7/1).
"I feel like I'm dreaming," said Delbonis.
"My key was to enjoy the match and enjoy playing this kind of player, because he's the best of all time."
Saturday's defeat will put the 31-year-old Federer under more pressure to justify that he can still be a major force in the sport.
He came into Hamburg, where he had triumphed four times, ranked at five in the world -- his lowest position since 2003 -- after his Wimbledon humiliation brought to an end a run of 36 consecutive Grand Slam quarter-final appearances.
Debuting a larger racquet frame this week, Federer had twice been pushed to three sets on his way to the semi-finals of the Hamburg claycourt event.
The Swiss squandered an early break lead against Delbonis and saved two set points in the 12th game to force a tie-break.
He was unable to convert his only set point at 6-5 and Delbonis took his fourth opportunity with a smash.
Federer was put under pressure early in the second set by the left-handed Delbonis, saving three break points in his opening service game and another in the sixth.
The Swiss had one chance to break Delbonis in the seventh game as the Argentine's composure slipped slightly and he let in costly unforced errors.
Federer was denied as Delbonis closed down the net, though, and again came out on the wrong side in the tie-break. Successive groundstroke errors from Federer at 4-4 gave Delbonis two match points and he converted his first as Federer netted a forehand.
Meanwhile, Fognini will be attempting to win his second title in as many weeks after claiming his first tour trophy last week at Stuttgart.