Federer, who has yet to drop a set in Halle after crashing out of Stuttgart in his first match back last week, limited his serve-and-volley game against the German who is a fine returner and Mayer was broken quickly as his opponent won the first set.
"I would say that's the best performance I've seen from Roger Federer this season", Barry Cowan applauds the 18-time Grand Slam champion after his ideal display of grass-court tennis in Halle. Federer advanced when Khachanov lifted a backhand long on match point.
Federer, 35, who has won eight times in Halle, beat the defending champion Mayer 6-3 6-4 in just an hour and six minutes.
"I thought it was extremely close, especially that second set", Federer said afterward.
The 20-year-old Zverev also had been 3-0 in title matches this season before Sunday, winning in Montpellier, Munich and Rome, where he beat world No. 2 Novak Djokovic for his first ATP World Tour Masters 1000 title. He tried his best to upset Federer's flow. "I'm still just very happy how I was able to close it out in the breaker".
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I don't know him that well yet so it's a match where I'll most likely focus on my own game.
Cilic then went on to play his doubles semi-final with Marcin Matkowski against Jamie Murray and Bruno Soares, which was moved onto Court One because of the rain delays, as he aimed to become the first man to win both titles at Queen's since Pete Sampras in 1995.
"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.
"It has been a hard year with a lot of practice, training and rehab so I am very happy to be back on the court", he said.
In Halle this week, Roger Federer analyzed the current situation his main rivals are going through and their recent results.
However, he was defeated by Alexander Zverev in three sets in the semi-finals at Halle in 2016.