In Sunday's final, 67th-ranked Govortsova will take on eighth-seeded Italian Francesca Schiavone, who crushed Ukraine's Alona Bondarenko 6-4 6-0 earlier in the day.
Just a handful of spectators turned out to watch the women's semi-finals after most of the top seeds and high-profile players were knocked out of the annual indoor tournament in the first two rounds.
Schiavone, however, paid little attention to a sparse crowd at the 12,000-seat Olympic arena, disposing of the 36th-ranked Ukrainian in just over an hour.
"I played better than her," said the 29-year-old, who was the highest women's seed to reach the quarter-finals.
"I was more aggressive and was dictating the points for most of the match, except for a short period late in the first set.
"I hope I can continue my good form in the final," added world number 24 Schiavone, who has lost nine out of 10 career finals, including the Moscow showpiece against France's Mary Pierce in 2005.
In the second semi, Govortsova took the initiative from the start by breaking Kleybanova's serve in the opening game.
The 20-year-old Muscovite, who stunned second seed and holder Jelena Jankovic in the previous round, looked in distress as she made 39 unforced errors, nearly twice as many as Govortsova.
"No, the match wasn't as easy as the score showed," Govortsova, 21, said after reaching her first final of the year.
"Nearly every game was close and I had to fight really hard to win it."
Russian third seed Mikhail Youzhny faces Kazakh qualifier Mikhail Kukushkin and sixth-seeded Serb Janko Tipsarevic plays Ukrainian qualifier Ilya Marchenko in the men's semi-finals later on Saturday.
(Editing by Sonia Oxley; To query or comment on this story email sportsfeedback@thomsonreuters.com)
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