The Russian, who won the French Open on clay last year, brought a 16-match winning streak on the surface into Madrid and was strongly favoured to coast past a player who has been dogged by knee injuries.
But she struggled at times in the first set before finding her range in the second.
Photos: Deepika Padukone, Neha Dhupia and Soha Ali Khan at event
In pictures: 15 facts about kissing that will surprise you
Birthday special: Shahid Kapoor's best performances in Bollywood
Photos: Kim Sharma, Sagarika Ghatge, Zaheer Khan at launch in Mumbai
Photos: Kangana Ranaut looks pretty in pink