Williams held up her end, dominant on serve throughout, but Frances Tiafoe was broken in the first set before Federer served it out in the second set tie break to seal the tie.
The Hopman Cup comprises two singles and a mixed doubles match between nations in a round-robin format with two groups of four.
Earlier, Federer beat Tiafoe 6-4, 6-1 in the men's singles before Williams levelled the tie with a comeback 4-6, 6-4, 6-3 victory over Bencic.
Earlier in the night, Williams raced out to a 3-0 lead in the opening set of her singles match, but Bencic won six of the next seven games to put her 37-year-old opponent on the back foot.
"It's great to back out here, I love playing Down Under here in Perth and in Australia, some of my best memories are here" Williams told Channel Nine after the match. "I made sure I kept focused on my serve and he gave me some errors at the end of the first set".
Federer and Bencic beat Britain's Cameron Norrie and Katie Boulter in their opening round-robin tie, while the United States of America lost to Greece on Monday despite Williams winning her singles tie.
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Sacramento swingman Bogdan Bogdanović then broke the hearts of Laker Nation when he hit a game-winning 3-pointer at the buzzer. James grimaced and grabbed his left groin before leaving the game for good and heading to the Los Angeles locker room.
"I'm looking forward to a great time". "It's been a while since I've been there", she said.
"I'll stay on the bike and keep the engine on", Federer said. I think his serve is super-underestimated.
Serena Williams and Roger Federer have been on the global tennis circuit for decades - both are 37 years old - and they have won 43 Grand Slam titles between them. The winners of each group play in Saturday's final.
The pair battled it out for over two hours in their first round match before Venus broke through in the sixth game of the decider to set up victory. In his press conference at the Hopman cup, Roger Federer spoke about his experiences of playing against, and with, quality women tennis players. Williams has called it a "dream come true", the BBC reports.
She is targeting Margaret Court's record of 24 Grand Slam titles and could secure that honour this season.