Sabalenka was beaten by Ekaterina Alexandrova at the WTA 1,000 event in Doha, while Gauff lost to Marta Kostyuk.
Russian Alexandrova, who beat Emma Raducanu in the first round, came from a break down twice in the third set and held serve twice against three-time Grand Slam champion Sabalenka.
The world number 26 then held her nerve in the third set tie-break to secure a 3-6 6-3 7-6 win.
The 30-year-old, who won a WTA Tour title in Austria last week, will play Belgium’s Elise Mertens in the last 16.
Ukrainian Kostyuk, the world number 21, fought back from 3-1 down in the second set to wrap up a 6-2 7-5 victory over Gauff in just 73 minutes.
It is a second successive defeat for Gauff, who received a bye in the first round and was playing for the first time since she lost to Paula Badosa in the quarter-finals of the Australian Open last month.
The 2023 US Open champion was undone by seven double faults and 39 unforced errors while she managed just eight winners.
