Evans, ranked 189th in the world, lost 7-6 (7-5) 7-6 (7-3) 6-3 against the 20-time Grand Slam champion.
"I think what's key is just going out there and playing really well, just doing the best that you can do", she said.
On an overcast day at Melbourne Park, second seed Angelique Kerber, the 2016 victor, and former US Open champion Sloane Stephens joined the big guns in round three, but the women's side also saw a top 10 player crash.
Federer also maintained his 100 percent record of reaching the third round at the Australian Open - 20 times in a row.
"For me personally was the first Grand Slam I have ever been selected too".
The unlucky soul facing him is Dan Evans of Britain, who won his first grand slam match since returning from a drugs ban earlier this week - in three sets against fellow qualifier Tatsuma Ito.
"It feels like playing a mirror a little bit".
He will have taken great heart from that victory, but.
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Roger Federer, victor of 20 Slams, says the new Japanese-made Dunlop balls behave differently in cooler night conditions and do not allow players to "out-spin" rivals.
Wozniacki also reached the third round with a 6-1, 6-3 straight-set win over Sweden's Johanna Larsson. "I think I can be happy how I got out of the blocks from the off-season", said Federer.
"I see why he can cause difficulties to players".
"Always helps if you sneak a quick break". Federer and Fritz met once before with multiple Grand Slam champ winning in three sets at an ATP tour event to defeat the upstart Fritz. During the win, Taylor Fritz served well as he won close to 70% of his service games which resulted in the American only losing 1 service game in the entire match.
He battled to save two set points at 5-3 down and then broke back to 5-5, outpointing Federer with an elegant one-handed backhand passing shot that the former World No. 1 would have been proud to call his own.
American teenager Amanda Anisimova has advanced to the third round at the Australian Open with a 6-0, 6-2 win over 24th-seeded Lesia Tsurenko.
"I thought I might have pulled away midway through the second set", added Federer. Tsitsipas could play Federer in the fourth round.
He returned to the ATP Tour past year and entered the Open as the world 189 but he will move up the rankings courtesy of making the second round.
For local fans, the progression of 19-year-old sensation Alex de Minaur was the highlight of day, with his gripping five-set thriller against Henri Laaksonen lasting just under four hours.