The Swiss looked a little off colour in the first set but a break at the death got the ball rolling and he thumped the American youngster 6-4 6-1 as he maintained his unbeaten start to the season.
The Hopman Cup includes a round-robin of two singles and a mixed doubles match between nations with two groups of four.
Williams survived a scare in her second match in as many days, eventually overcoming Belinda Bencic, 21, 4-6 6-4 6-3 after squandering a 3-0 lead in the first set.
Williams - who has amassed her honours across singles, doubles and mixed doubles - added: "It was so fun". Bencic broke back in the seventh game after a volley error from Serena and she was the player to beat in the rest of the set, breaking again at love in game nine and delivering the opener after a service victor in game 10, rattling off the last five games.
The 37-year-old will face off against rising star Frances Tiafoe in Tuesday's tie against the United States, before playing Williams in the mixed doubles.
"I'm looking forward to a great time". "She played really well".
"I'm happy in all aspects of my game that things were working - foot work, offensive play, serve, return - it was all there". In his press conference at the Hopman cup, Roger Federer spoke about his experiences of playing against, and with, quality women tennis players.
New Horizons to return images of Ultima Thule flyby
From New Horizons' location, a radio transmission traveling at light speed requires just over six hours to reach Earth. The encounter with Ultima Thule will be brief and technically demanding, even more so than New Horizons' Pluto flyby .
As of Monday afternoon, the match had generated enormous buzz among tennis enthusiasts ― which isn't surprising given that Federer and Williams have collectively won 43 Grand Slam titles.
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 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.
"It is very exciting for both of us and I hope a lot of tennis fans tune in and watch it", said Federer after opening his Hopman Cup campaign with an easy singles win yesterday. Hearing your stories makes me know I can do this.
And Williams has expressed her amazement at how Federer copes with two sets of twins.
Federer's response? "It's the age of social media", he said, laughing at the prospect of Williams' plan.