The former top-20 star looked anything but a player on the comeback trail from a serious knee injury as she routed American teenager Clervie Ngounoue 6-0 6-2 in little more than an hour.
Rinky Hijikata also progressed in vastly different fashion on a promising opening day for the Australian contingent in New York.
Hijikata vindicated his wildcard entry with a 7-5 5-7 6-3 7-5 victory over Russian Pavel Kotov in a sapping contest stretching a minute shy of four hours.
The hard-earned victory was the 22-year-old's first at a grand slam outside of Australia.
Saville broke 17-year-old Ngounoue seven times, never faced a single break point on her own serve and finished with 16 winners and just 13 unforced errors for the match.
"I was very composed," Saville said after notching her first win at Flushing Meadows in five years.
"When the day started I was pretty relaxed. I don't know why - it doesn't really happen on day one of a grand slam.
"Warming up before the match I was like 'umm, this feels like just a normal match' and that felt nice and I think that is why I played well."
Playing the Open on an injury-protected ranking after being sidelined for more than eight months, Saville knows she will need to find another level against Swiatek on Thursday (AEST).
"Well, the biggest goal is not to get double bagelled," she said.
"I am excited. Hopefully we'll get to play on the big court. When I was coming back from injuries that was like the goal - get to play on all the bigger courts at every slam and hopefully that will be ticked off.
"I think I can still make her life very uncomfortable. I will just play free and see what happens.
"Forehand is my weapon and, when it's working, this is when I am dangerous.
"Obviously I have to move well to get to use my forehand but today I also served pretty well, hit my spots well. It is part of my game hunting forehands."
While Saville and Hijikata rolled on, fellow Australians Kim Birrell and wildcard Storm Hunter bowed out in the first round.
Birrell, a qualifying lucky loser, battled hard in a 6-3 7-6 (7-4) loss to 2021 Australian Open finalist Jennifer Brady, while Hunter succumbed 6-4 6-0 to Czech 10th seed Karolina Muchova, the 2023 French Open runner-up.
Ajla Tomljanovic, Olivia Gadecki and Alexei Popyrin also play on day one at Flushing Meadows.
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