Having started the match with the unexpected tactic of returning Federer's serve from well back beyond the baseline, Zverev experienced more success charging the net and taking the ball early, quickly breaking back to force a first-set tiebreak.
Federer barely put a foot wrong, winning 7-6 (7-3) 6-4 6-4 in almost two hours to set-up a fourth-round match against Grigor Dimitrov.
The Swiss will face Grigor Dmitrov in the fourth round, another fabulous hitter who is often compared to Federer.
History did not favour Zverev.
But Federer had admitted prior to this match that he was unsure of what to expect from Zverev, a left-handed serve-volleyer who famously dumped Andy Murray out of this year's Australian Open, and it wasn't long before the German hit back. In Halle in 2013 he did not even manage a game, while their two matches this season were closer but not that close.
But in spite of his poor record against Federer, Zverev was unfazed as he found himself 4-1 down in the first.
For the third time in the match the 29-year-old dropped his second service game in a set to put Federer on the front foot, and he became less and less of a threat on the third seed's serve.
In an nearly flawless copy of the second set, Federer focused on holding his serve and wasted little energy on his way to the next round.
There was a bit of an exhibition feel about Federer in the final stages before he clinched victory with his 13th ace.
Roger Federer is coming off a straight sets win over Mischa Zverev that took 33 games to decide.
"With me, I hoped I was going to be there". "I didn't go through it myself even though that would be quite an experience, I guess". "He is at the flawless age right now to really understand his game, he is physically very strong, and I think mentally he has really taken that next step".
Federer has been battling a cold but is confident he will be fully restored to health by Monday.
"I'm feeling better. I'm definitely feeling better". I'm very happy anyway.