The Britons fought back to win 3-4 (2-5) 4-3 (5-4) 4-1 in Perth after Norrie had stunned Tiafoe in the singles and Boulter had lost to Williams.

GB were already eliminated from the team event but the win is a confidence boost before the Australian Open.

The first Grand Slam of the year starts on 14 January in Melbourne.

Britain finished their Group B campaign with two wins and a loss but it is not enough to progress to the final, with defending champions Switzerland having already booked their place.

They can, however, take great encouragement from their showing here, having followed up their surprise opening victory over Greece with this win over much higher ranked opponents.

World number 90 Norrie started the day with a 7-6 (7-4) 6-0 victory over Tiafoe - who is ranked 51 places above him - before world number 97 Katie Boulter put up a fight in the second set of her 6-1 7-6 (7-2) defeat by former world number one Williams.

"She's a champion so to actually share the court with her is such a privilege," Boulter, 22, said.

The United States failed to progress from the group after three defeats, despite 23-time Grand Slam champion Williams winning all three of her singles matches here.

The 37-year-old, who was watched by her one-year-old daughter Olympia from the stands, said the event had been great preparation for her bid to win an eighth Australian Open title.

"It was perfect - it's just like this in Melbourne," Williams said on the tournament website.

"It's the exact same sun and it gives me so many problems. After you serve, you are blind for the next two points."