"It has been a hard year, I have spent a lot of time on practice, training and rehab so it is nice to be back on court", said Federer, who suffered a surprise defeat by Tommy Haas in Stuttgart earlier this month.
But, instead of serving out the set, the top seed was broken again and Khachanov even held two set points at 6-5 before the world No. 5 recovered and forced a tie-break.
He converted his first match point to reach an 11th Halle final.
Switzerland's Roger Federer, right, with the victor trophy and Germany's Alexander Zverev, left, with the trophy for the second place, frame model Eva Herzigova, after the final match of the Gerry Weber Open tennis tournament in Halle, Germany, Sunday, June 25, 2017.
Federer defeated Zverev's older brother Mischa in the second round this week.
The Swiss master stormed to his latest victory - a fourth in as many finals this year - in just 53 minutes and appears in prime form with little more than a week to go until he begins his pursuit of an eighth Wimbledon crown. "I think he deserved to win", Zverev said. Zverev, a young rising star in men's singles, had a strong week at the tournament.
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It was a closely-fought encounter, as the two players, who know all about each other's game, went full tilt into the match. However, he could not hold the higher ranked player as Kidambi extended his lead to 11-9 at the break of the second game.
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Gasquet will now play the victor of the last quarter-final between local favourite Alexander Zverev and Spaniard Roberto Bautista-Agut later on Friday.
"I was doubting myself a little bit, I must admit, because losing [in the opening] round for the first time in 15 years on grass was always going to shake me a little bit and it did", Federer said.
His huge serve was on full display when he won the 's-Hertogenbosch title on grass last week and once again he used it to devastating effect against Querrey.
This is going to be a fun match between these two talented players, as Zverev is growing up before our eyes and Federer is, well, Federer.
The 35-year-old, defeated in his first comeback match in Stuttgart last week, took control from the start with an early break and kept world number 12 Zverev on his toes.
Zverev, who beat Federer in the Halle semifinals last year, fell to 3-1 in finals this year.
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