Elsewhere in Dubai, Gauff suffered a third successive defeat as she fell to world number 53 Kessler.
Third seed Gauff, 20, started the year on red-hot form, winning nine matches in a row.
However, since losing to Paula Badosa in the quarter-finals of the Australian Open, Gauff has lost in the second round at the Qatar Open and Dubai Tennis Championships after receiving a bye in the first round at both tournaments.
Kessler saved five of the six break points she faced against her fellow American before wrapping up a 6-4 7-5 victory in one hour and 29 minutes.
It is the first top 10 victory of her career, while the 25-year-old is also into the third round of a WTA 1,000 event for the first time.
World number one Aryna Sabalenka claimed a 6-3 6-4 victory over qualifier Veronika Kudermetova, while second seed Iga Swiatek stormed past two-time major winner Victoria Azarenka in a 6-0 6-2 win.
Jasmine Paolini continued her title defence with a 6-2 7-5 victory over Germany’s Eva Lys, while Ons Jabeur fell to a 7-6 (8-6) 6-4 defeat by American Peyton Stearns.
Sixth seed Elena Rybakina beat Moyuka Uchijima 6-3 6-2 to set up a last-16 meeting with world number 10 Badosa, who won 6-2 6-1 against Elise Mertens.
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