Roger Federer and Stan Wawrinka will face off in the Australian Open semi-final
Stan Wawrinka is a clutch player now and I have to stay aggressive
The 35-year-old Swiss produced a brilliant tactical display to overcome the unusual serve-volley technique of Zverev and knows he cannot afford to rest on his laurels when he faces Wawrinka.
"I have to stay aggressive," said Federer.
"The more time I give him the better he is, like most of the big hitters.
"He's maybe the biggest hitter we have in the game right now.
"I'm happy that he's got this far but he doesn't need to go one step further!"
Roger Federer was in full flow against Mischa Zverev
Wawrinka is the 2014 Australian Open champion and also came out on top in his last major, beating Novak Djokovic in the US Open final back in September.
And Federer believes Wawrinka, who will be playing in his eighth Grand Slam semi-final, has all the tools to send him back home.
"He's a clutch player now," added Federer.
"He's really turned it round and he proved that again at the US Open.
Mischa Zverev stood no chance as Roger Federer, 35, rolled back the years
"He's won a slam the last three years.
"When it was important in the Davis Cup he was right there for me, for us and for Switzerland."
The two countrymen have faced each other 21 times in competitive matches but the world No 4 Wawrinka has only triumphed on three occasions, all of them coming on clay.
But even before Federer faces the 31-year-old, he admitted that he did not expect to be in this situation, having missed the whole of the second half of 2016 with a knee injury.
"I thought I was maybe going to win a few rounds depending on the draw, and maybe get to the fourth round or the quarter-finals," Federer said.
"When I saw the draw, everyone was calling it a dream draw – I didn't see a dream draw at all!"
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But the early departure of Murray and Djokovic means Federer is now bookies' favourite to win the tournament.
His greatest threat from the bottom half of the draw will probably come in the form of old rival Rafael Nadal.
However, the Spaniard must come through a tough quarter-final against No 3 seed Milos Raonic tomorrow night first.