Chasing an 18th grand slam title, and first since 2012, the 35-year-old Federer neutered his left-handed German opponent's serve-volley game to set up a last-four meeting with fellow Swiss Stan Wawrinka.
"I think it definitely went as good as it possibly could have gone," Federer told reporters.
"I had to adapt my style. It was a nice match. I think I played great."
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Looking in form as imperious as in his heyday of a decade ago despite missing the back half of last season after knee surgery, Federer is now one match away from a potential final against his old rival Rafa Nadal.
Wawrinka, the 2014 champion, will want to have a say about that as will Nadal's quarter-final opponent, Milos Raonic.
But with both Williams sisters also still standing in the women's draw, it would be easy to imagine it was 2007 not 2017 at Melbourne Park.
Zverev's serve-and-volley game is a throwback to an even earlier era and the world number 50 contributed fully to an entertaining, if brief, contest with his fine volleying and net play.
The unorthodox game helped the left-hander beat world number one Andy Murray on Sunday, one of two stunning upsets along with the early exit of Novak Djokovic which have opened up the draw for Federer and Nadal.
Against Federer, though, it took Zverev 15 minutes to hold serve and get on the scoreboard and by that stage he was already 5-0 down in the opening set.
"I think he did not really let me play," said Zverev. "He just has so many more options, how he can, like, outplay me or pass me. It was different, definitely different."
LEAPING BACKHAND
The Swiss needed four more minutes to wrap up the set with a leaping backhand at the net but Zverev gradually found his touch and broke for 3-1 in the second set.
Federer broke again straight awayy but Zverev, who admitted after beating Murray that he had no Plan B, continued to charge to the net to greater and greater effect.
The Swiss bided his time, though, and a couple of brilliant backhand passes gave him another break before he served out the set with less than an hour on the clock.
A third set studded with deft shot-making went with serve until another Federer backhand gave him a break for 5-2 and a rasping crosscourt winner, his 65th of the match, sent him into a 41st grand slam semi-final.
"I'm happy, I never thought I was going to be this good," Federer said. "And here I am, still standing, in a semi against Stan, it couldn't be cooler for the both of us.
"I think him and Rafa know my game best. Stan and I practised so much together. Yeah, I guess those two guys know me very well."
Federer has been such an extraordinary player that he has all but lost the ability to shock with his feats on court.
Andy Roddick, who was inducted into the tennis Hall of Fame on Tuesday and lost a Melbourne semi-final to Federer a decade ago, offered some welcome perspective.
"Everyone here is going to talk about it in every story they write for the rest of this tournament, and I still don't know if that's enough," the American told reporters. "It's pretty amazing."
(Editing by Ed Osmond)
