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Some will view her 5-7, 6-1, 6-1 win as patchy and at times, disappointing.
However, Barty showed when the going gets tough - as it will given her predicted draw over the next two weeks - she gets going.
Tsurenko was ranked as high as 23 last February, so the Ukrainian was always going to test the Australian.
But it was Barty who fended off the disappointment of losing the first set to storm into the second round, dropping just two games from then on.
The last Aussie woman to win the Open was Chris O’Neil in 1978 and Barty is essentially carrying the hopes of a nation.
But a couple of things I’ve learned about Ash - since first coming across her as a young teenager at Futures events on the Australian Pro Tour - is her relaxed demeanour and will to win.
“I think you have to fight no matter what the score is,” Barty said after her victory.
“Whether you're down in the first set or down and kind of almost out of it, I think it's important to try and fight for every single point.”
“This (the Australian Open) is probably the moment I have been looking forward to the most through the off-season."
Next up for Barty is Polona Hercog, with a rematch against her 2019 Australian Open conqueror Petra Kvitova on the horizon in the quarter-finals.
The Aussie could then face last year’s champion Naomi Osaka in the semi-final.
But for now, Barty is just trying to deal with the “chaos” of her home slam.
"Slams always feels like there's a lot of chaos going on because there's so many people," she said.
"It's busy with singles and doubles and mixed players, coaches and families. It's just chaos.
"We're just going along for the ride and trying to play some good tennis."
And as shown by her French Open triumph last year LIVE on SBS - if there’s one player Australia can count on to deal with this chaos, it sure is Ash.