The top-seeded Federer, who is returning to fitness after missing the French Open with a back injury, raced away with the first set against the fifth seed but completed victory in one hour and 21 minutes after saving five set points in the second.
"I thought it was my best match thus far," Federer said. "It is a good win for me and I'm clearly very happy to be in the semis."
Next up for the 34-year-old will be Zverev, the 19-year-old who continued his breakthrough season with a 7-6(9) 6-3 win over Marcos Baghdatis of Cyprus.
Federer was impressed with his young opponent, saying: "He's got a big serve, he's got a nice backhand, he's improving his forehand and he's moving forward. He's going to be a tough player in the future, no doubt about it."
The other semi-final will see third-seeded Austrian sensation Dominic Thiem, who is seeking his fifth title of the season, against German Florian Mayer, who beat Italian Andreas Seppi 7-6(4) 6-3 in his quarter-final.
Thiem hoped to repeat his win over Philipp Kohlschreiber in last weekend's Mercedes Cup final but the German pulled out before their last-eight match with a left hip strain.
(Reporting by Ian Chadband; Editing by Toby Davis and Ken Ferris)
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