It was not easy for the four-time Grand Slam winner against Kenin but she eventually triumphed 7-6(2), 6-2 after a one-hour and 51-minute slog in draining conditions on Rod Laver Arena.
It was a replay of the 2020 French Open final that Polish star Swiatek won, and they had not met since.
"It wasn't the easiest first round. She played really well. I tried to find my rhythm, especially in the first set," said the world number one, who owns three Roland Garros crowns and another at the US Open.
"I'm happy at the end of the set I could win the most important points."
Victory stretched the 22-year-old's unbeaten streak to 17 matches, the second-longest of her career, after she finished 2023 by winning 11 straight in Beijing and Cancun, which took her back to world number one.
She then won five more matches at the United Cup at the start of this season, meaning she was in imperious touch coming to Melbourne.
There will be no let-up against next opponent Danielle Collins, who eased past 2016 champion Angelique Kerber in three sets.
Swiatek's best showing in Melbourne was the semi-finals in 2022, when Collins swept past her 6-4, 6-1.
"I can't say that I have easy draw here, I'll try to do my best," she said. "Danielle is a really good player. We played really tight matches."
"On the other hand our last match was pretty - I mean, from the score, I had it under control," she added, referring to Cincinnati last year where she dropped just one game.
"Every match is different. I'm not going to anticipate anything. I'm just going to be ready and we'll see."
Swiatek opened with a serve to love against 2020 champion Kenin, who has slid down the rankings to 41. But the American woke up and broke before holding to surge 3-1 clear.
With her left thigh strapped, Kenin was returning well and her backhand was on fire.
But she wobbled in the sixth game, with back-to-back double faults gifting Swiatek a break back for 3-3.
Undeterred, Kenin earned another break with a searing backhand to move 5-4 ahead only to falter again serving for the set.
It went to a tiebreak, where the top seed stepped up to get over the line after a marathon 68 minutes.
The second set was equally tight until game five, when Kenin slapped a forehand wide to hand Swiatek two break points and she converted when the American pounded a backhand long.
It was a killer blow, with Kenin having nothing left in the tank as the world number one sprinted to the finish line.
