(REUTERS) - Agnieszka Radwanska showed why she should be considered among the favourites for the Australian Open later this month by beating world No. 1 Serena Williams in the final of the Hopman Cup in Perth on Saturday.

The Polish world No. 5 claimed a 6-4, 6-7 (3-7), 6-1 win to put her country 1-0 up in the mixed team event. But John Isner beat Jerzy Janowicz 7-6 (12-10), 6-4 to draw the United States level, with the mixed doubles later on Saturday.

"When I go and play against her, you have nothing really to lose, she is No. 1 in the world and a great champion," Radwanska told reporters of her beaten foe. "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 earlier this week in the round robin, could have done with some advice from the 18-time 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 No. 1 broke back to force a tie-break that she took 7-3.

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

The Australian Open begins in Melbourne on Jan 19.