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Hesse lost the first set, but she won 4-6, 7-6, 6-3 to win the surprise victory of the US Open and the Australian Open.
It came Exit Osaka After the withdrawal Serena WilliamsThe title winner eight times, due to a left knee injury.
This is the second time in a row that Serena has retired from the competition. Indian Wells Championship Last week because of the disease.
Earlier, Czech world number two Petra Kvetova needed three sets before beating Croatian Donavikic in the third round.
Cvetova, two-time Wimbledon champion, won 6-4, 3-6, 6-4 in two and a half hours.
Kvetova will meet Frenchwoman Caroline Garcia in the fourth round.
Garsia beat the German Jolie Georgis 15, 6-0, 7-5.
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Hesse lost the first set, but she won 4-6, 7-6, 6-3 to win the surprise victory of the US Open and the Australian Open.
The Osaka exit came after Serena Williams, the eight-time winner, retired due to a left knee injury.
This is the second time in a row that Serena has retired from the Indian Wells Championship because of her illness.
Earlier, Czech world number two Petra Kvetova needed three sets before beating Croatian Donavikic in the third round.
Cvetova, two-time Wimbledon champion, won 6-4, 3-6, 6-4 in two and a half hours.
Kvetova will meet Frenchwoman Caroline Garcia in the fourth round.
Garsia beat the German Jolie Georgis 15, 6-0, 7-5.
