Elsewhere in Berlin, world number one Aryna Sabalenka beat Swiss Rebeka Masarova 6-2 7-6 (8-6) in a match that took place across two days.
The Belarusian took the first set on Wednesday before bad light forced play to be suspended.
Sabalenka, beaten by Gauff in the French Open final, returned on Thursday and came back from a break down to wrap up a straight-set win.
Sabalenka will face Kazakh Elena Rybakina in the quarter-finals after the former Wimbledon champion beat Czech Katerina Siniakova 6-4 7-6 (7-5).
Marketa Vondrousova, who won the Wimbledon title in 2023, beat Russian Diana Shnaider 6-3 6-7 (3-7) 6-3.
Elsewhere at the Halle Open, Russian Andrey Rublev was another big name to fall, failing to convert two match points in a 3-6 7-6 (7-4) 7-6 (8-6) loss to Argentine Tomas Martin Etcheverry.
But German world number three Alexander Zverev recovered to beat Italian Lorenzo Sonego 3-6 6-4 7-6 (7-2).
