The Ukrainian conceded only her second set in seven matches this year but ultimately found a way past her Czech opponent 4-6 6-2 6-1 as the temperatures soared on Rod Laver Arena.
"It was very tough for me today," the 23-year-old said.
"I didn't feel good and hopefully I can recover and be ready for next match. I had some issues before the start of the (tournament), it was like big question that I'm going to step on court for my first round."
The next match will be against 15-year-old compatriot Marta Kostyuk, the 521-ranked qualifier who doubled down on her maiden grand slam victory on Monday with a 6-3 7-5 win over local Olivia Rogowska on Wednesday.
"First time I heard about her when she won here," said Svitolina. "It's pretty cool that I'm playing someone from my country. It's gonna be very exciting for me and hopefully I can be ready for that match."
Svitolina had been firming as one of the favourites in a wide open race for the Melbourne Park crown after winning the Brisbane International warm-up event.
Her first set performance against Siniakova clearly sounded a warning to Svitolina about letting any kind of complacency creep into her head as she earned six break points but failed to convert a single one of them.
World number 59 Siniakova, who also took Svitolina to three sets at the U.S. Open last year, really went for her shots, hitting 11 winners, and it was she who managed to get the upper hand in an arm-wrestle of a 50-minute set.
Svitolina finally got her first break at the eighth attempt to go 2-0 up in the second set.
Siniakova never gave up but was not the same threat after a seven-minute medical timeout in the second set and Svitolina claimed the victory with an unreturnable serve after two hours and 14 minutes.
"The second and third set was 6-2 6-1, but I felt like it was 7-6 in the third or 8-6 in the third," Svitolina
"It was very tough for me today. Not feeling great and was not focused on the right things."
(Reporting by Nick Mulvenney in Sydney, editing by Amlan Chakraborty/Peter Rutherford)
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