Sabalenka, the Australian Open champion from Belarus, was beaten 6-2 7-6 (2) by Veronika Kudermetova despite improving after an error-strewn start. Gauff lost 6-4, 6-0 to Ekaterina Alexandrova.
"For me it's very important to play like that today," Kudermetova said. "I always believe in myself. I know I can play really well, and I always believe."
Both Sabalenka and Gauff were playing their first tournament on grass - and their first since the French Open - while their Russian opponents reached the final of the grass-court Libema Open in the Netherlands on Sunday, which Alexandrova won.
They will now have a rematch in Berlin for a place in the semifinals against either Caroline Garcia or Petra Kvitova.
Gauff had the edge early on with a 3-1 lead in the first set before losing 11 of the next 12 games as Alexandrova dominated.
"Maybe the score looks easy, but it's never like that because she played amazing," said Alexandrova, who won her seventh straight match.Â
"I needed to stay focused during every single point to keep it that way. I'm just hoping I can keep this form as long as I can."
Players from Russia and Belarus are returning to Wimbledon next month after they were barred last year following the Russian invasion of Ukraine.
Marketa Vondrousova booked her place in the quarterfinals when her opponent Jule Niemeier retired while losing 6-3, 6-5 after injuring her wrist in a fall.
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