Ajla Tomljanovic is refusing to get carried away about the possibility of a blockbuster showdown against Serena Williams at the US Open.

The Aussie emulated Williams with a first round win on the opening day in New York, to set up a potential third round clash if both players can get through their next matches.

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Tomljanovic's 6-3 7-6 (7-5) defeat of Czech Karolina Muchova was somewhat expected, given the Australian No.1 had backed up her latest run to the Wimbledon quarter-finals with nine wins in three weeks on American hard courts.

Williams on the other hand, rode a wave of euphoria from a raucous home crowd inside Arthur Ashe Stadium to down Danka Kovinic in a drama-charged straight sets win.

In contrast to Tomljanovic's victory, there was more hope than expectation around Williams' result on the back of some patchy form heading into her farewell tournament.

Regardless, Williams's stirring 6-3 6-3 triumph over Kovinic keeps the prospect of a third round match against Tomljanovic alive - in what would be the first ever head-to-head between the pair.

While Tomljanovic admits it's a tantalising prospect, the 29-year-old is desperate not to think any further ahead than her second round clash against unseeded Russian, Evgeniya Rodina.

"For me, the next one is going to be a really big task just because I've been in a few situations where I've had a non-seed and someone would say it's a good draw and it would kick me in the arse because I would think about it," Tomljanovic said.

"So I'm taking that as an opportunity but at the same time I'm trying to approach it like I haven't done before.

"So I'm not even thinking about it (Williams).

"But it would be cool because I've never faced her so I don't want her to retire and me not ever have played her."

Serena Williams faces World No.2 next up

Even if Tomljanovic does win as expected in the second round, a third round clash against Williams is far from a certainty, with the American champion facing a tough task next up against World No.2 Anett Kontaveit.

Open officials went to extravagant lengths to prepare for the 40-year-old's farewell on Monday evening in New York, creating an electric atmosphere inside world tennis' biggest arena and inviting a galaxy of global stars to Arthur Ashe Stadium.

Bill Clinton, Mike Tyson and Hugh Jackman were in the full house as the 23-time grand slam-winning legend produced a vintage display to defiantly fend off retirement for at least another two days.

For Tomljanovic, the Aussie's win came against a potentially dangerous opponent in Muchova, who has the distinction of being the last woman to beat Ash Barty at Melbourne Park - in the 2021 quarter-finals.

Tomljanovic - who arrived in New York believing "anything can happen" - was suitably relieved after repelling a second-set fightback to advance in one hour 48 minutes on rowdy Court 7.

"No matter how well I was playing going into this tournament, playing the first round of a grand slam it's almost like starting from scratch," Tomljanovic said.

"With your game, with your emotions so this is always the toughest task for me, getting through the first round."

Aussie compatriot Daria Saville earlier ran out of steam in a 3-6 6-2 6-4 first-round loss to Romania's Elena Gabriela Ruse.

Saville was backing up from the final in Quebec on Saturday and said she felt "a bit cooked" after the tight turnaround and a schedule of five matches in a week.

with AAP

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