Agnieszka Radwanska showed why she should be considered among the favourites for the Australian Open later this month by beating world number one Serena Williams and helping Poland to its first Hopman Cup title in Perth yesterday.

World number five Radwanska claimed a 6-4 6-7 6-1 win to put her country 1-0 up against the United States and returned to partner Jerzy Janowicz and beat Williams and John Isner 7-5 6-3 in doubles as Poland became the 13th nation to win the mixed team event.

Isner had overcome Janowicz 7-6 6-4 in the other singles to haul the US back into the contest.

“When I go and play against her, you have nothing really to lose, she is number one in the world and a great champion,” Radwanska told reporters of her singles victory.

“It doesn’t matter what the score is. It’s never over, she’s a great fighter. I’m just very happy that I could come back after that second set and play my good game in the third set.

“Wins like this always give a lot of confidence.”

Radwanska’s first victory over Williams in nine meetings comes after she signed up former American great Martina Navratilova as a coach.

Williams, who also lost to Eugenie Bouchard, of Canada, last week in the round robin, could have done with some advice from the 18-times grand slam singles champion after struggling in the opening set.

The American’s forehand was particularly troublesome, contributing to many of her 28 unforced errors as she was broken twice early on to fall 4-1 behind before losing out 6-4.

The second went with serve as Radwanska pushed and pulled Williams around the court, with the powerful American retaliating by bludgeoning some heavy winners in an even contest.

The Pole, a semi-finalist at the Australian Open last year, then broke Williams to go 6-5 up and serve for the match but she was unable to put the American down as the world number one broke back to force a tiebreak that she took 7-3.

However, that was as good as it got for Williams, who will be seeking a 19th grand slam title in Australia, as she collapsed in the third to allow Radwanska to claim the moral boosting win.

The Australian Open begins in Melbourne on January 19.