Victory gave world number three Federer, the oldest player in the top 10, three wins from three singles matches in Perth as he geared up for the season's first Grand Slam as a favourite alongside Novak Djokovic, Rafa Nadal and Alexander Zverev.
"He could be my son," 20-times major winner Federer joked about the age between him and Tsitsipas, before praising the world number 15.
"He did a nice job. I think we both played well without too many mistakes. I learned about his game. From my game, I didn't learn anything.
"For me, it's about maintaining a good level of play. I'm happy where my game is at. And I was impressed with what I saw from Stefan."
Greece, who needed a 3-0 win to progress at the expense of Switzerland, finished with a 2-1 consolation victory. The Swiss topped Group B having already beaten Britain (3-0) and the United States (2-1).
Maria Sakkari beat Belinda Bencic 6-3 6-4 before Greece claimed the mixed doubles match.
Earlier, Serena Williams notched up another singles win but could not prevent the U.S. from losing 2-1 to Britain for their third defeat that left them bottom of the standings.
Following wins over Sakkari and Bencic, Williams made it three from three with a 6-1 7-6(2) victory over world number 97 Katie Boulter.
The 37-year-old will resume her quest for a record-equalling 24th major in Melbourne and was pleased with her preparations in hot and humid Perth.
"It was perfect. It's just like this in Melbourne. It's the exact same sun and it gives me so many problems," Williams, who competed in her first tournament since losing the U.S. Open final last September, said.
"After you serve, you are blind for the next two points. It was good to play three matches here, singles, not to mention the mixed doubles."
Cameron Norrie defeated Frances Tiafoe 7-6(4) 6-0 to make it 2-0 to Britain before teaming up with Boulter to win the mixed doubles dead rubber.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Christian Radnedge)
