Dellacqua and Ash Barty combined to lead Australia to a 3-2 victory in a World Group II Fed Cup tie against the Ukraine in front of 3108 at the Canberra Tennis Centre on Sunday.

The pair outclassed Ukrainian twins Nadiia and Lyudmyla Kichenok 6-3 6-4 to send Australia to a World Group play-off on April 21-22, and celebrate Dellacqua's 33rd birthday in style.

Should Australia win that, they will be promoted to the World Group for the first time since 2015 ahead of the 2019 Fed Cup.

The capital quickly became a happy hunting ground for Australia with captain Alicia Molik declaring "it's a place we would love to visit in the future".

Dellacqua would certainly have no qualms with that after experiencing "one of the best moments" in her storied career.

"It's more just the occasion playing at home, not knowing how much longer I will play for, not knowing how many more of these moments I'll get," Dellacqua said.

"I really appreciate the moment and the experience, it's definitely one to remember. I had a message from Sam Stosur this morning, it was about a tie that we had played when we had a live rubber in Slovakia.

"She reminded me how good that moment was and this tops that. Being here at home in Canberra and playing for your country, it's definitely one of the best moments in my career.

"Once we knew that we were going to have to go out there and play, there was such a calm feeling. I knew that we'd get the job done to be honest, I had such confidence and faith in us as a team that we were going to get the job done."

World No. 26 Barty had gifted Australia a 2-1 tie lead to start the day when she beat 15-year-old sensation Marta Kostyuk but things threatened to go awry soon after.

Unranked singles player Nadiia Kichenok shocked Australian Daria Gavrilova in the final reverse singles rubber, as the Ukrainian blasted 21 winners in a thrilling 4-6 6-2 6-3 win to send the tie to a doubles decider.

What's more stunning is Kichenok wasn't even slated to play Gavrilova until just before the match - Ukraine sprung a late surprise and called her in to replace her sister Lyudmyla Kichenok.

But a frustrated Gavrilova had endured a poor weekend, with Barty and Dellacqua proving a much tougher task for the Ukrainian sisters.

"I was really emotional [after my match], and I was really emotional just then too because this win means so much as a team," Gavrilova said.

"I'm really happy right now but I was crying so much after the match. I had a cold shower and I was like 'okay you've got to be there for your teammates' and I was going nuts for them.

"I didn't have the best singles matches, to be honest I had two shockers, but I'll learn from that and I'm sure my teammates are going to support me which they always have and I'll learn from this experience."

Ukraine were left to rue the absence of their two best players in world No. 3 Elina Svitolina and No. 40 Lesia Tsurenko.

But Australia could only beat the players in front of them and Molik's confidence never wavered despite a rocky road to the finish.

"I knew we were going to get the job done too in the doubles," Molik said.

"It's funny, when you believe and trust in someone or a pairs ability, there's a real quiet calmness, and I have to describe that as the feeling in the locker room before the doubles. It was almost inevitable.

"Casey and Ash created that, and they created that in the way they've gone about their tennis for so many years now."