The 37-year-old Federer is warming up for the Australian Open, which he has won for the last two years.
"He came up with some big shots, but so did I and managed to hold my nerve", he said.
"This was a great start but obviously a long way to go here and in Melbourne", Federer said. "It's nice that I'm feeling as good as I am and played a wonderful match against Cameron".
No 4-ranked Zverev beat David Ferrer 6-4, 4-6, 7-6 (0) in the men's singles match before the German pair combined to win the mixed doubles 4-2, 4-3.
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It also marks the return of temperamental Nick Kyrgios, the defending champion who has been talking to psychologists and "trying to get on top" of his mental health after another roller-coaster year. Indeed for those who do not remember, Federer has played right here with his wife Mirka; watch the amusing interview from back then below. "I only know her from some champions' dinners at Wimbledon", Federer said. "I was not missing any rhythm", the tournament website cited Federer as saying after the 57-minute win.
Federer breezed past Norrie in the first rubber, winning 6-1 6-1, before Bencic beat Boulter in two sets to clinch victory.
"The footwork, the offensive play, serve, return, it was all there, so I think it was a great match for me".
Switzerland will play the United States on the New Year's Day, when Federer will play against Serene Williams in the mixed doubles. Later on, Team Switzerland won also the mixed doubles 4-3 4-1 to complete a ideal day.
And the 37-year-old is looking forward to the mixed doubles clash with the U.S., where he will face off against 23-time grand slam victor Serena Williams. "What he has done in tennis over the past 15 or 20 years has been absolutely incredible".
"He is the greatest fighter, maybe, that we have ever seen in tennis".