In a rematch of their US Open fourth-round match in which Swiatek had to recover from a set down before going on to ultimately win the tournament, Niemeier gave Swiatek problems again with her power and ability to utilise the fast conditions.
An even first set saw Swiatek unable to find a break point until she was 5-4 ahead, before forcing two set points, eventually taking the second as a strong forehand could only be returned into the net.
Niemeier came out in the second set determined to make amends, though, breaking Swiatek in the opening game as she looked to overwhelm the Pole.
The 23-year-old belied her status as the world number 69, causing the top seed problems as she mixed power hitting with some nice drop shots but, as she served for the set, Swiatek turned up the dial and forced the break to level at 5-5.
After holding her own serve it looked like the second set would head to a tie-break, but Swiatek's increase in intensity made the difference again as some expertly placed deep and wide shots caused another break as she sealed a straight-sets win.
"Honestly I wanted to be focused on myself because she can serve amazing," Swiatek said in her on-court interview. "She uses fast conditions so I just wanted to think what I could do to push her back.
"I'm pretty happy I got through this match because the fist round is always tricky and playing Jule is always tricky."
Data slam: Swiatek takes advantage of second serve
Niemeier's serve gave Swiatek problems throughout, but the Pole was ruthless when she was given rare opportunities.
Despite a success on her first serve of 71 per cent (32/45), Niemeier could only win 35 per cent on her second (9/26).
Swiatek – 20/28
Niemeier – 18/29
Swiatek – 0/3
Niemeier – 3/1
BREAK POINTS WON
Swiatek – 3/5
Niemeier – 1/3