American Gauff, who has been unwell with a stomach virus, will drop from third to fourth when the updated world rankings are released, with Poland’s Iga Swiatek replacing her.
The reigning French Open champion was ruthless in the second set after losing the first and looked a safe bet to advance to the next round at the expense of Noskova, after breaking the 21-year-old for a second time in the third set.
But world number 13 Noskova produced an impressive comeback in front of the Spanish crowd as Gauff faltered and will face Ukrainian Marta Kostyuk in the quarter-finals on Wednesday.
Kostyuk, 23, won 6-2 6-3 against American Caty McNally to celebrate her ninth victory in a row and back-to-back Madrid quarter-finals.
“Sometimes I get lost on court, especially in the second [set], as it happened today,” said Noskova. “I had to find my rhythm all over again in the third [set].”
Meanwhile, Sabalenka will take on American Hailey Baptiste, who defeated Belinda Bencic 6-1 6-7 (14-16) 6-3 in her fourth-round match, on Tuesday.
She defeated Baptiste, 24, in the quarter-finals of the Miami Open on her way to winning the title last month.