The 36-year-old six-times champion may have been giving away 16 years to the man tipped to be the next superstar of the game but Federer proved in a dominant third set that for the moment he remains a cut above his young pursuers.
The triumph in 2 hours 11 minutes puts the 19-times grand slam champion in Saturday's semi-finals -- the 14th time he has made the last four in 15 appearances -- with the tournament still only three days old.
It also meant that Zverev and Jack Sock, who earlier battled from behind to beat Marin Cilic 5-7 6-2 7-6(4), will now meet on Thursday to decide the other qualifier from the Boris Becker group.
Federer's win ensured Cilic, once again a disappointment at the season-ending tournament, was eliminated. World number two Federer is now an overwhelming favourite for a seventh crown in the absence of Rafael Nadal, who has pulled out injured.
(Reporting by Ian Chadband; Editing by Toby Davis)
