The 37-year-old will face off against rising star Frances Tiafoe in Tuesday's tie against the USA, before playing Williams in the mixed doubles.
The Swiss maestro had talked before the match of his nervousness at facing the feared Serena serve and his fears seemed confirmed as he was unable to cope with two deliveries in her opening service game, but thereafter he took control of the match with Bencic. The two greats will be opponents for the first time in the mixed doubles.
"I mean the guy is the greatest of all time, both on and off the court", she said.
There has always been a debate over whether Roger Federer or Serena Williams is greater but the Swiss added another feather to his cap in what's likely to be the only meeting between the pair during their professional careers.
"My fellow moms and dads working- or stay home it's equally as intense- but you inspire me".
Serving at 4-2, Serena fends off two break points and bringing the game home with an ace before a solid hold in the ninth game that sent her over the finish line and kept the United States of America in contention.
"I guess what you're seeking here is confirmation to see is everything there that you thought there was, or is there any fixing still to be done in the coming weeks".
Williams enjoyed a strong opening service game in the mixed doubles, with two of her serves proving too hard to handle for Federer. Belinda has done it in the past so I'm sure she's going to pass me on the information that I need to know about Serena's serve and all the other shots that she has.
Only the group winners advance to the final, so the closing doubles could ultimately decide the victor of a group that also contains Greece and Britain.
The pair posed together for a selfie after the match.
World No.3 Roger Federer has been left feeling reassured that his game is in good shape after opening his Hopman Cup campaign with a 6-1 6-1 demolition of Cameron Norrie. "I knew I could play better", she said. In his press conference at the Hopman cup, Roger Federer spoke about his experiences of playing against, and with, quality women tennis players.
He and teammate Bencic are the defending champions at Hopman.
"It was definitely a relief", Williams said of the result.