But that is one of only two WTA titles she has picked up in 17 years on tour and she has never gone beyond the third round of a Grand Slam in 13 attempts, while Gauff managed that in her debut Major last year.
But Gauff, as you would expect sometimes from a 15-year-old, struggled mentally on Thursday.
She made a nervy start, slipping to 0-40 in her opening service game, before being broken by the 31-year-old Siegemund.
The German had a plan to move her around and it worked.
Drop shots brought her to the front of the court, while angled ground strokes pulled her to either side.
Gauff struggled for consistency, dumping a series of forehands into the net as her timing was off.
Both players exchanged breaks, with Gauff letting out a guttural roar after a sequence of hard-won points.
At one stage she was two points away from conceding the first set, but dug her way of that hole and took out the set after the longest rally of the match.
Siegemund called for her coach at that point, and his advice worked, as the German took the second set with relative ease, breaking the Gauff serve four times.
The teenager was struggling to stay composed, and often let the frustration get the better of her.
That pattern continued into the third set. Gauff was broken early, and spent most of the set remonstrating with herself. There were bright moments, but punctuated by too many unforced errors.
She hit seven double faults and was broken eight times, with a final error on match point summing up her day.
Siegemund will play Williams in the quarter-finals on Friday.
