Gauff earned her 50th win of the year in WTA matches as she beat Magda Linette 6-0, 6-4 while Sabalenka defeated Magdalena Frech 6-2, 6-2.
"We've played a lot of matches in the past, a lot of great battles. I'm really excited," said Sabalenka, who has won three of her seven previous meetings with Gauff.
Three-time Grand Slam winner Sabalenka wielded her powerful forehand to great effect as she broke twice to build a 4-0 lead, then held her own serves to secure the first set.
Poland's Frech tried to fight back in the second set, getting her first break when she was 3-0 down and almost made it 3-3 but Sabalenka saved two break points to retain her lead and broke again to ensure victory.
"I (had) to be on from the beginning. I'm glad I was able to win this match in two sets," Sabalenka said.
Sabalenka's next opponent Gauff was equally dominant earlier in the day, saving four break points and winning 67% of her return points as former Australian Open semi-finalist Linette fell to a bagel in the first set.
Gauff, who made eight double faults in the match, faced a tougher battle in the second set but one of Linette's 22 unforced errors gave the American an edge in the seventh game as she got the only break of the set, which sealed the win.
"I played well ... overall, maybe two bad games," Gauff said in the post-match interview after extending her winning streak to nine matches.
Third seed Jasmine Paolini of Italy plays fifth seed Zheng Qinwen from China in another quarter-final later in the day. The winner will take on China's Wang Xinyu, who beat Russia's Ekaterina Alexandrova 4-6, 7-5, 7-6(6) in the last eight.
