"I was happy I was able to come back in that second set and break back. That was an important moment, for sure," the Polish top seed and hot favourite told reporters at Melbourne Park.
"First match of a first Grand Slam. So always tough. Jule is not an easy opponent, so I'm happy I'm through and going to be able to play more matches here."
The first set had been deadlocked on serve when Swiatek finally forced a break to creep over the line 6-4 in 52 minutes.
But the 21-year-old was immediately broken at the start of the second and struggled for consistency, before getting the job done.
"My goal in my next matches is not to get into that situation," she said. "I need to have more intensity."
The Pole insisted she could still take positives from the victory.
"It showed me that I don't have to feel 100 percent to win a match."
Niemeier was coming off the biggest season of her career in 2022, where she made the quarter-finals at Wimbledon and led Swiatek by a set and a break in the last 16 at the US Open.
But the 23-year-old faltered when serving at 5-4 and Swiatek pounced to level before taking the match.
"Honestly, I wanted to be focused on myself because I know that Jule serves amazing and was really pushing, putting pressure on me," said Swiatek, who landed only 49 percent of her first serves.
The victory took her win-loss record in first-round Grand Slam matches to 15-1, a year after recording her best result at Melbourne Park, losing to Danielle Collins in the semi-finals.
The three-time major winner -- she also triumphed at Roland Garros in 2020 -- will face Colombia's Camila Osorio in the second round.