World number 114 Delbonis stunned former world No. 1 Federer 7-6 (9), 7-6 (7) to set up a title clash against Italy's Fabio Fognini, who beat third seed Nicolas Almagro of Spain 6-4, 7-6 (1) in the other semi-final.
Federer, ranked 5th in the world, wasted an early break of serve in the first set before he was force to save two set points and force the set into a tie-break, which was won 9-7 by the Argentine.
Federer struggled with his serve in the second set as he saved three break points in his opening service game and then was made to save another break in the sixth.
The Swiss also missed a golden opportunity to break Delbonis in the seventh game as the second set also went into the tie-breaker which the youngster won 7-4 to clinch the match as Federer hit the forehand into the net.
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