World number 192 Mayer had not claimed an ATP singles tournament victory since back in 2011 before seeing off fellow-German Zverev 6-2 5-7 6-3 in Halle in a triumph for experience over youth.
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Zverev, ranked 38th, won his 27th match of the season after losing to Federer in their first meeting last month in the Rome second round.
“It’s unbelievable to get a win against Roger, especially on grass”.
Zverev hit back in the second, taking a 2-0 lead and saving two match points when the unseeded 32-year-old Mayer had the chance to serve for the tournament before setting up a decider. “Don’t forget that that final is a very big match for me as well”.
Federer was playing a 12th consecutive Halle semi-final but missed out on an 11th straight win at the event in a town where both a street and a hospital kitchen are named in his honour.
5-7, 6-3 to reach only his second ATP Tour final after being beaten by Dominic Thiem on clay in Nice last month.
With the win, Zverev became the first teenager to beat Federer since the current world number three fell to Andy Murray at the Masters 1000 event in Cincinnati in 2006.
Watched by his coach Ivan Lendl, a two-time champion at Queen’s Club, Murray forced a forehand error to break for 2-1, fought off four break points in the next game and broke at love to take the opening set.
At London: ATP Aegon championships: Semifinals: Andy Murray bt Marin Cilic 6-3, 4-6, 6-3; Milos Raonic bt Bernard Tomic 6-4, 6-4.
The German could yet meet World No. 7 Thiem, 22, in the final again this time as the Austrian faces another home player in Florian Mayer in Saturday’s second semifinal.
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The top seed saved two break points in the eighth game with aces and secured a late break to win the set.
