US vs Switzerland gets underway with Federer facing Tiafoe at 9.30am with Williams' singles match against Bencic scheduled to take place at 11am.
The 91st-ranked Norrie was coming off an impressive win over world number 15 Stefanos Tsitsipas the previous day, but had no answer to the brilliance of the Swiss maestro, ranked third in the world.
Attention soon switched to their much-hyped New Year's Day clash against Switzerland, where Williams will share a court with Roger Federer and his partner Belinda Bencic in the mixed doubles. For Tennis Tonic, I mostly take care of the sections that we call Quick Buzz and Videos that is about brief stories, videos or posts about the top Tennis Players.
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Though the 23-time Grand Slam champion won 7-6 (7-3) 6-2, she felt some soreness in her ankle and required a medical timeout at the end of the opening set.
Although thrilled with his first-up performance, Federer doesn't want to get carried away just yet.
"Of course, it is just the beginning and I am quite happy with how I played", Kerber said.
Last year's runners-up Germany made a triumphant return when Alexander Zverev and Angelique Kerber recorded hard-fought victories in their singles matches. "I only know her from some champions' dinners at Wimbledon", Federer said.
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The 37-year-old knows he will have to go to Melbourne Park in peak form given that top-ranked Novak Djokovic, who won the Mubadala World Tennis Championship on Saturday with a 4-6, 7-5, 7-5 win over Kevin Anderson, has set overhauling Federer's mark of 20 majors as his "objective".
Williams then found her range and dominated the tie break to wrap up the first set in 63 minutes.
However the Spaniard wasn't going to let her own five-match winning run against the German go easily, and took the second set.
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"This was a great start but obviously a long way to go here and in Melbourne", Federer said.