Sakkari hit nine aces and 23 winners, while Kenin had no aces and only eight winners. The loss was Kenin's third in 14 career quarterfinal matches.
"I was rushing a little bit too much in the beginning of the match," Sakkari said. "I was hitting too big when I didn't have to, but I'm glad that once again I found a way to just turn the match around."
Sabalenka finished last season with titles at the Ostrava and Linz indoor tournaments and has started 2021 with four wins in Abu Dhabi. Sabalenka has won three of the four matches she has played against Sakkari, all of them on hard courts.
Svitolina twice came back from a break down in the deciding set, including when Kudermetova served for the match at 6-5, but trailed 3-0 in the tiebreak and couldn't recover.
Kudermetova will play Marta Kostyuk in the semifinals, with both players looking to reach what would be their first career tour final.
Kostyuk, an 18-year-old Ukrainian, lost the opening seven games of her match against Sara Sorribes Tormo before winning 0-6, 6-1, 6-4.