The Wimbledon winner saw a forehand from the Argentine fourth seed as wide, but didn’t get an overrule from the chair after the South American saved the match point in question.
When tournament supervisor Paolo Pereira wouldn’t bend on the issue either, Federer calmly went back to work after speaking his mind.
He lost his second winning chance seconds later from a return long, but finally came good for the victory - his 15th in a row - and a third match point in the tie-breaker when Gaudio sent a backhand out.
World Number three Federer said contesting what he perceived as an injustice was a point of honour in front of a roaring home crowd under perfect sunny skies in the Alps.
“I looked at the ball twice, it had to be out,” said the Swiss. “But they said I waited too long after the point to question it. Nevertheless, I had to say something, it was such an important point.”
Federer is set for his first Gstaad final in six appearances Sunday, where he will face Czech third seed Jiri Novak.
The former champion warmed up for a shot at a second trophy here as he dismissed doubles partner Radek Stepanek 7-5, 6-1.
He says all of the pressure will be on Federer when they meet.
“Roger’s a great player, I have nothing to lose,” said the 28-year-old who has yet to lift a title this season. “Everything is going for him here - the crowd, the atmosphere, the court.
“He’s playing at home and he knows this place well. But I don’t care who I play. I’m in the final. I only need to look after my game and play my best tennis. I don’t have to worry about who’s on the other side.”
Federer ripped through the opening set in little more than 20 minutes, but knew the rout couldn’t last as clay ace Gaudio - 22nd in the points race, showed why his 31 wins this season on clay are the most on the ATP.
The pair traded breaks in the third and fourth games of the second before the tiebreaker. Federer called his week after Wimbledon “unbelievable.”
Results semifinals:
Roger Federer bt Gaston Gaudio 6-1 7-6 (8-6); Jiri Novak bt Radek Stepanek 7-5 6-1.
BASTAD (Sweden): Results from the 380,000 euros ATP Swedish Open tournament on Saturday:
Semifinals: Mariano Zabaleta b Carlos Moya (Spain) 2-6 6-3 6-4
Quarterfinal: Tommy Robredo bt Filippo Volandri 6-4 6-4.
PALERMO (Sicily): Quarter-final results from the $110,000 Palermo International WTA tennis tournament on Friday:
Katarina Srebotnik bt Yuliana Fedak 7-5 2-6 6-1; Dinara Safina bt Francesca Schiavone 6-3 6-2; Ludmila Cervanova bt Henrieta Nagyova 6-1 3-6 7-5; Anabel Medina Garrigues bt Virginie Razzano (France) 2-6 6-1 7-6 (7-3).—Reuters