Kuznetsova is already assured of her best year-end ranking since 2009 and is aiming to defend her Moscow title in front of a home crowd.
However, the 25-year-old was hoping to be fit to compete in the WTA Finals after moving into the eighth and final qualifying place when Serena Williams opted to pull out last week because of a niggling shoulder injury. "I finally relaxed and began to play my normal tennis", Kuznetsova said.
Kuznetsova is now in 10th place on the Road to Singapore rankings and so needs to win the Moscow title again to edge out Great Britain's Johanna Konta.
"It was really good for me that we had to play the third set".
Australia's Daria Gavrilova has continued her strong form with a 6-2 6-2 first-round upset of Lucie Safarova at the Kremlin Cup.
Mourinho Praises Paul Pogba Like Only Mourinho Can
He knows what he wants and the levels are high, so he always wants to keep up the pressure. I only bring the players [to the press conference] that are going to start.
Russia's two-time Grand Slam title victor won 6-1, 6-7 (2/7), 6-4 to level her record with Svitolina, who was seeded fourth, at 1-1. Gavrilova led 3-0 in the second when Suarez Navarro made a decision to withdraw.
The 22-year-old needed just 59 minutes see off Konjuh, breaking her serve five times in the match.
In the other semi-final, Julia Goerges of Germany, who saw off eighth-seeded Daria Kasatkina of Russian Federation 7-5, 6-1, will clash with Australia s Daria Gavrilova, who beat Anastasia Pavlyuchenkova, seeded seventh, 7-5, 4-6, 6-3.
Cuevas beat Slovak qualifier Jozef Kovalik 6-4, 7-6 (4), firing 11 aces in their second-round match.
Wildcard entry Steve Darcis of Belgium rallied to beat Benoit Paire 6-7 (6), 6-1, 6-4.