Roger Federer will face Rafael Nadal in a final for the first time in 2 1/2 years on Sunday at Basel, Switzerland.
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The top-seeded Federer eased to a 6-3, 6-4 win in 64 minutes against unseeded Jack Sock of the United States in the semifinals.
Gasquet needed seven break points to take a 1-0 lead in the second, and Nadal levelled when the fifth-seeded Frenchman served for the set leading 5-4.
Third-seeded Nadal trailed by a set and a break before getting his third three-set win this week.
Federer and Sock has faced each other only once in the round of 16 clash of the Indian Wells Masters earlier in the year.
The 29th-ranked American reeled off three straight returns for winners to stun Federer and break serve for the only time.
“I thought the match was close”, Federer said.
Nadal, who has enjoyed a return to form after a relatively poor year by his standards, fell just short of claiming only the second indoor hard court title of his career. They last met on court for an Australian Open semifinal that Nadal won in three straight sets in January 2014.
Seventeen-times grand slam champion Federer now trails Nadal 23-11 in their head-to-head series.
Federer came under pressure in his first service game as Nadal tried to get an early lead, but the Swiss dug deep to save a break point. There were no real surprises there, I was match-ready. And showing comic timing as sweet as a few of his shots, he jested: “A little bit less today – but I understand”.
Federer dominated the first half of the match, finding the lines with his ground strokes and commanding at the net, but he was broken at 5-5 in the second set and Nadal forced a third.
Gasquet could still have denied Ferrer a place in the ATP World Tour Finals next month, but his defeat means Ferrer, along with Japan’s Kei Nishikori, complete the eight-man line-up for the season-ending showpiece.
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Swiss Indoors is Federer’s home tournament and the former world number one holds the record for winning the tournament for the highest number of times.
