Niemeier took the opening set from reigning French Open champion Swiatek and threatened to stage the upset of the tournament after scoring the first break of the second set with a crosscourt forehand.
Monday marked the first time Swiatek, the player to beat in women’s tennis this year, had dropped a set this tournament.
But the world No. 1 came back from a shaky start to beat Niemeier 2-6 6-4 6-1.
By the fifth game of the second set, Swiatek took four straight points, finishing with an ace, a forehand winner and another ace, before breaking the German in the next game.
“I’m just proud that I didn’t lose hope,” Swiatek said. “I had a hard time pushing her back. I’m pretty glad it worked. I used my experience to keep my level the whole match.
“Honestly at the beginning [of the second set], I felt like I’m just making a little bit less mistakes, but she also started playing less aggressively,” Swiatek, who broke Niemeier’s serve seven of 13 times, added.
“It was easier for me to just play the ball in. Yeah, I think I started being more solid and I used a little bit more of the chances that I had.”
With the win, the Polish champion keeps her streak alive of not losing to a player outside of the top 100 at a grand slam event, according to the WTA.
Next up, Swiatek will take on American Jessica Pegula.
CNN’s George Ramsay contributed reporting.