Tomljanovic's victory came after Daria Saville had continued a stirring comeback to breeze through her first-round 6-1 6-2 against Valentini Grammatikopoulou, declaring how she was now after the Australian No.1 spot.

But Tomljanovic, current holder of that accolade, then demonstrated why she's still the tops in the post-Ash Barty era, out-battling a potential nightmare opening opponent in fifth seed Estonian Kontaveit.

"It's up there definitely," Tomljanovic said as she pondered whether her 7-6 (7-5) 7-5 win was the best of her grand slam career.

And the Croatian-born Tomljanovic was thrilled by the performance of her Russian-born pal Saville, wondering if it could spark a new friendly rivalry for the domestic No.1 spot.

"I knew that 2022 was going to be a big year for her and I definitely welcome the competition, and especially with Dash," Tomljanovic said.

"We're pretty good friends, so it's all in good spirits, but I think we both definitely will fight for it.

"So it will be a nice one!"

In a red, white and blue outfit she said had been designed to get the home crowd on her side, Tomljanovic had her right thigh still heavily strapped after having to retire from last week's Morocco Open quarter-final.

"But I was going to give everything today, no matter even if I was in pain and I luckily wasn't," world No.42 Tomljanovic said.

"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.

"And I definitely, I was like, 'if I lose this I want her to beat me with her best tennis and not give her cheap points'."

She was as good as her word, making only 12 unforced errors to Kontaveit's 25.

She'll next play Varvara Gracheva, and will recognise the danger after the Russian knocked out another Australian, Astra Sharma, on Sunday.

At the start of a damp day, Saville had wasted no time advancing into the second round.

It took the 28-year-old less than an hour and a quarter to beat the Greek qualifier - and the Paris rain - with the win that will leapfrog her above third-ranked Maddison Inglis and current Australian No.2 Sharma when the new rankings are released.

"I don't look at rankings so don't tell me!" laughed Saville, who's made extraordinary progress since returning from 10 months out following surgery to deal with a chronic achilles injury.

Yet at the same time, she couldn't help admitting: "One of my goals is to be the number one Aussie."

On a rain-disrupted day, Sydney's indomitable James Duckworth, back in action in only his second tournament since a ninth surgery, this time on his hip, was deeply unimpressed by his 6-2 6-4 6-2 loss to Sweden's Mikael Ymer.

In Australia's match of the day, Jordan Thompson simply had no chance against 13-time champion Rafael Nadal, who steamrollered his way through their first-round clash, 6-2 6-2 6-2, on Court Philippe Chatrier.

John Millman was left to fight another day when rain forced a suspension of his match after American 27th seed Sebastian Korda had broken for a 1-0 lead.

Australian Associated Press