A capacity crowd of 14,064 turned out for the tie, and they saw Federer and Bencic largely capitalise on the mixed doubles inexperience of Williams' teammate, Francis Tiafoe, to clinch the deciding rubber under the Fast4 format, 4-2, 4-3 (5/3).
Williams and Federer, both 37, faced off in a mixed-doubles exhibition match at the Hopman Cup on Tuesday.
Switzerland will defend its unbeaten record against Greece in its final round robin match Wednesday with the United States taking on Britain.
Williams dropped the first set but recovered to beat Federer's Swiss team-mate Belinda Bencic 4-6, 6-4, 6-3.
Williams looked sluggish early in her singles match, and needed her left ankle re-strapped after winning the first set. The second set took just 22 minutes as Tiafoe's game imploded, with the world No 39 also struggling to maintain a high intensity.
Roger Federer and Serena Williams, two of the greatest tennis players of all time, found the ideal way to welcome in the new year.
'Great champion, you can see how determined and focused she is - I love that about her'.
"He is just amazing.the greatest of all time", Mrs Gethin said, her eight-year-old son Archie standing next to her with Switzerland's red cross on his T-shirt.
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He crossed the border in Arizona several years ago and had worked a variety of jobs as a labourer, including at several dairies. During a news conference on Friday, Christianson spoke out strongly against California's sanctuary laws.
Federer and Williams, of course, won't be the only players on the court in a mixed doubles match.
Both Federer and Williams say they're excited about the historic matchup. "This is super cool that we get to do it at such a pinnacle point of our careers", she said.
"It was a great experience, I'm sad it is over I was just warming up", she joked. "I know how to play through pain and maybe also my game, the way it's built, the free-flowing game that I have, allows me to stay away from some injuries because I'm not too tense on the court".
"It's great to be back out in match day, and it's great to be back out here", Williams said.
"But today I felt really comfortable playing the rallies".
Williams led 4-1 in the first set before Bencic fought back to win the next five games.
Federer opened his Hopman Cup campaign in flawless style, crushing world No.91 Cameron Norrie 6-1 6-1 in 57 minutes.
Federer eventually clinched it for reigning champion by claiming the winning point in the truncated tiebreak used in mixed doubles with a ideal angled volley.