Belinda Bencic defeated Katie Boulter 6-2, 7-6 (0) in the women's singles to clinch the match before Federer and Bencic teamed up to prevail over Norrie and Boulter 4-3 (4), 4-1. Williams, representing the USA, will play with Frances Tiafoe, while Federer will compete alongside Swiss player Belinda Bencic.
If those matches are finished in relatively standard time then the mixed doubles match between Federer/ Bencic and Williams/ Tiafoe is scheduled to start at 12.30pm.
"I've played with some of the greatest doubles players in the world in Martina Navratilova and Martina Hingis, and I've also played against some of the best in Venus and other great ones in the past".
Two breaks of the serve in each set were enough for the 20-time Grand Slam victor to win 6-1, 6-1 in just 57 minutes, just over two weeks out from the year's first Grand Slam.
'The ankle is good I just was struggling: it was too tight, it was too loose and I ended up having to change my shoes but it's fine now, ' she said.
"A bit of polish is needed but it was nice to come out and play a pretty clean match", Barty said.
This year's tournament is expected to be Perth's final Hopman Cup and Tuesday's group tie is an early sellout on the back of the prospect of seeing two of the all-time greats, with 43 grand slam singles titles between them, on the same court.
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A similarly star-studded contest took place earlier on Sunday as Alexander Zverev and Angelique Kerber of Germany saw off Spanish pair David Ferrer and Garbine Muguruza.
In the dead mixed doubles rubber, the Germans made it a clean sweep with a straight sets win.
The fancied Greece kept its tournament alive with a 4-1, 1-4, 4-2 victory in the mixed doubles after an opening defeat against Britain.
That proved to be the start of a productive year for a resurgent Kerber, who won at Wimbledon and climbed back to number two in the world. She broke twice in the second set and closed it out with an ace.
Federer faced three break points in his first service game, but was near ideal from that point on as he wrapped up the contest in 57 minutes at RAC Arena on Sunday night.
This was a great start, but we've got a long, long way to go here and in Melbourne.