Niemeier took the opening set from reigning French Open champion Swiatek and threatened to stage the surprise of the tournament after earning 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, dropped a set at the tournament.
But the world No. 1 bounced back from a shaky start, beating Niemeier 2-6 6-4 6-1.
In the fifth game of the second set, Swiatek grabbed 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 give up hope,” said Swiatek. “I had a hard time pushing them back. I’m pretty glad it worked. I used my experience to keep my level throughout the game.
“Honestly at first [of the second set]”I felt like I was just making a little less mistakes, but she also started playing less aggressively,” added Swiatek, who broke Niemeier’s serve seven out of 13 times.
“It was easier for me to put the ball in. Yes, I think I started to get more solid and I took a little more chances that I had.”
With the win, the Polish champion is keeping up her streak of not losing to a player outside the top 100 in a Grand Slam event, according to the WTA.
Next Swiatek meets the American Jessica Pegula.