The 34-year-old's best grand slam run before last week had taken her only as far as round three at the All England Club in 2015, but she is now one win away from a Centre Court final after edging Niemeier in an entertaining 4-6 6-2 7-5 triumph.
Niemeier, at the opposite end of her career at 22, was making her main-draw Wimbledon debut and had looked on course to ride her momentum into the last four.
In only the third all-German grand slam quarter-final of the Open Era, Maria's nerves showed in the first set as she immediately dropped serve and was unable to recover.
But after quickly being broken again at the start of the second, the veteran seized control, battling back as Niemeier appeared to lose her composure.
The decider could have gone either way, with one crucial point going in Maria's favour as Niemeier dived headfirst after a drop shot at the end of a 13-stroke rally, yet experience told at the last.