The Swiss legend’s four-year old son was in the player’s box at the Rod Laver Arena as Federer won 6-2, 7-5, 6-2 against American youngster Fritz.
That sets the 37-year-old up with a clash with Greek star Stefanos Tsitsipas in the round of 16 on Sunday.
Federer’s family travel across the world with him to Grand Slams, with the world No 3 having twin daughters – Myla and Charlene – in 2009 and then twin sons, Leo and Lenny, in 2014 with his wife Mirka.
And Lenny was present to watch him alongside his coach Ivan Ljubicic and Mirka up in the stands, with the star’s children not often spotted inside the arenas.
Talking on-court after his win, Federer was asked by Eurosport’s Jim Courier: “One thing that was interesting about this match that I don’t recall seeing, we’re watching your player’s box and one of your sons came out and watched the entire first set.
“I can’t tell if it was Leo or Lenny because they’re twins but who was it and did you know he was going to come out and watch?”
And Federer responded: “No I didn’t even know he was going to come to the stadium!
“When I peaked over and he was sitting there I was like, ‘Oh wow, okay, an extra special guest for me!’
“Back in the day it was playing in front of your parents, then playing in front of your friends is special, then famous people, musicians.
“At the end playing in front of legends is a thrill and then it’s back to basics and playing in front of your family.
“That’s what it was today. For me it was a very special match. I’m happy Lenny was there in the first set today.”
And Federer – who won the Australian Open 12 months ago for his 20th success at a major – added on his victory: “I think I wanted to get out of the blocks quickly because I knew the threat of Taylor, his possibilities on the serve and what he could do on the return, especially second serve.
“I think I had extra focus today to really make sure I got off to a good start and I did.
“Then second set was tight, was tough, there was a few chances.
“But he protected his serve well and it was close at the end. We had some tough points and it was good fun.
“I think I had a really good feeling out here today against someone who can definitely be very dangerous for the future and I wish him the very best for the future.”
Federer, who is chasing his 100th career title, has reached at least the semi-finals in all of the last three years and seven of the last eight – winning the Open in the last two years.