The world number 18 disposed of the Russian wildcard with a convincing final-set performance after she was pegged back by her unfancied opponent.
The Czech player, who has four career WTA Tour titles to her name, will next take on compatriot Klara Zakopalova who beat Alexandra Cadantu of Romania 6-3 6-3.
Former French Open champion Francesca Schiavone is out though after being convincingly beaten by Poland's Urszula Radwanska 6-3 6-1.
Although none of the WTA Championship qualifiers are competing in Moscow this year, the Kremlin Cup still has a fine field, featuring three former Grand Slam champions, two former world number ones and the defending champion, Dominika Cibulkova.
Meanwhile, two seeds fell on the opening day of the WTA Luxembourg event.
Seventh-seeded Austrian Tamira Paszek lost 6-3 7-6(8) to Czech Lucie Hradecka while eighth-seeded Spaniard Carla Suarez Navarro crashed 7-6(2) 6-4 to Magdalena Rybarikova of Slovakia.
The sole seed to progress was ninth seed Mona Barthel who was too good for local player Mandy Minella in a 7-5 6-0 win.
The top seed in Luxembourg is Roberta Vinci of Italy.
WTA Moscow results
Urszula Radwanska (Poland) beat Francesca Schiavone (Italy) 6-3 6-1
Klara Zakopalova (Czech Republic) beat Alexandra Cadantu (Romania) 6-3 6-3
8-Lucie Safarova (Czech Republic) beat Margarita Gasparyan (Russia) 6-3 4-6 6-2
Sofia Arvidsson (Sweden) beat Bojana Jovanovski (Serbia) 6-2 6-4
WTA Luxembourg results
9-Mona Barthel (Germany) beat Mandy Minella (Luxembourg) 7-5 6-0
Lucie Hradecka (Czech Republic) beat 7-Tamira Paszek (Austria) 6-3 7-6(8)
Monica Niculescu (Romania) beat Romina Oprandi (Switzerland) 7-6(4) 6-1
Magdalena Rybarikova (Slovakia) beat 8-Carla Suarez Navarro (Spain) 7-6(2) 6-4
- Alexandra Cadantu