Kharkiv, Kharkiv Oblast, Ukraine, 12 February 2017 | AAP

Australia’s hopes of returning to the head table of women’s tennis are hanging by a thread after Alicia Molik’s team lost the opening singles rubbers of their Fed Cup World Group II tie against Ukraine in Kharkiv.

Ash Barty took the first set against world No.13 Evina Svitolina before Svitolina won the match 4-6 6-1 6-2.

Barty raced through her opening service game in the second set but from then on it was all one-way traffic as the Taiwan Open champion won 11 consecutive games to take the second set in 24 minutes and set up a commanding 5-0 lead in the third.

“I’m unhappy with the result but I did the best I could today,” Barty said.

“You have to go out there with the true belief that you’re going to win. If you ask anyone they’ll always say ‘yeah I think I can win’ but you have to truly believe it.

“My serve is one of my main weapons and I think it let me down a little bit today. But I’m certainly not discouraged and we’ll give it a red-hot crack tomorrow.”

Molik was full of praise for Barty.

“If you didn’t know anything about tennis and watched that first set you’d think she (Barty) looked like the No.13 player in the world,” she said.

Molik said she was confident Barty and former world doubles No.3 Casey Dellacqua would be able to get the job done given the opportunity.

“That would be a dream,” she said.

“In the doubles we’re really confident. I hope for Casey that the team can get it to that point. It’s not really the result we wanted today.”

Earlier, Daria Gavrilova was defeated in straight sets by Lesia Tsurenko.

Tsurenko kept her perfect record against Gavrilova intact with a 6-2 6-3 win.

Gavrilova will face long-time friend Svitolina in Sunday’s opening rubber before Barty and Tsurenko do battle ahead of the potentially decisive doubles clash.

Gavrilova broke Tsurenko’s serve in the first game but that was as good as it got for Australia’s No.26, who was unable to maintain the form which saw her make it to the fourth round of the Australian Open last month.

The Ukrainian broke back almost immediately and took the first set with ease in 31 minutes.

Again Gavrilova broke in the opening game of the second but she was unable to capitalise, losing the set in 43 minutes and was visibly frustrated after the match.

For more details, visit our dedicated Australia v Ukraine Fed Cup tie page.