Sevastova, who is world No. 64, broke Gauff's serve to claim the first set. The American hit back soon after, edging the second set to level the match. However, Sevastova raced to victory in the final set, twice breaking Gauff's serve as the American racked up five double faults.
Gauff secured a superb comeback victory against seventh-seed Elise Mertens on Tuesday, winning 0-6, 7-6(4), 7-5 on a busy day of play after the tournament was washed out on Monday.
Elsewhere, top seed Aryna Sabalenka dominated American Alison Riske in a 6-1, 6-4 victory to advance to the quarterfinals. The world No. 4 took just over an hour to dispatch Riske, serving 10 aces to bag a comfortable win.
Information from Reuters contributed to this report.