Australia’s new No.1 women’s player, Ajla Tomljanovic, has cast aside her past on-court demons to score one of the biggest victories of her career at the French Open.

Tomljanovic, the world No.42, stunned fifth-ranked Estonian Anett Kontaveit 7-6(7-5) 7-5 to cap a day of major casualties at Roland Garros.

The Croatian-born 29-year-old ascended to her adopted nation’s top billing after Ash Barty’s shock retirement in March and is set to battle it out with resurgent Daria Saville to hold that spot.

Fellow naturalised Australian Saville also moved into round 2 with a dominant 6-1 6-2 defeat of Greek qualifier Valentini Grammatikopoulou, after Jason Kubler advanced a day earlier.

Tomljanovic has faltered several times from winning positions against the game’s biggest stars, especially at grand slams, including Simona Halep at last year’s Australian Open.

There was a fear history was repeating itself when she stumbled while leading Kontaveit by a set and 4-2 – but she recomposed herself to break a five-all deadlock and clinch the huge upset.

“It’s up there, definitely,” Tomljanovic said, on whether it was the greatest triumph of her grand slam career.

“There were a few key moments where I really could have mentally lost it a little bit and when it was happening, I felt like this is where I’ve screwed up in the past.

“I was like, ‘If I lose this, I want her to beat me with her best tennis and not give her cheap points’.”

Tomljanovic told News Corp in January that her shift in mindset began at Wimbledon last year, when she overcame a similar situation against France’s Alize Cornet on her path to the quarter-finals.

She next faces Russia’s Varvara Gracheva, who ousted Australia’s Astra Sharma in round 1.

Kontaveit joined No.2 seed Barbora Krejcikova, Naomi Osaka, Reilly Opelka, Stan Wawrinka and Liudmila Samsonova on the clay-court scrap heap.

But Sydney’s Jordan Thompson was unable to engineer his own titanic upset, falling 6-2 6-2 6-2 to 13-time champion Rafael Nadal in a 122-minute rout.

Paris’ wet weather postponed John Millman’s tough opener against 27th seed Seb Korda, with the American having broken for a 1-0 lead.

Meanwhile, Tomljanovic’s career-best Wimbledon run could come at great cost, given the ATP and WTA stripped ranking points from this year’s event because of the ban on Russian and Belarusian competitors.

That controversial stance was in protest of those countries’ invasion of Ukraine.

Tomljanovic said the points situation was “very unfair” but she confirmed, unlike countryman Chris O’Connell, that she would contest Wimbledon despite the “very strange” circumstances.

“There’s no reason why I couldn’t have actually successfully defended (my points),” she said.

“I would have loved to have had that opportunity, because there’s pressure there that you want to embrace when you’ve done really well the year before.

“I wouldn’t miss it for the world. Wimbledon is Wimbledon – and if you win it and get no points, of course, you’d still take it.

“But I’m definitely going into that small bracket of players who are going to be really affected.”