Schiavone suffers shock loss in Barcelona
The Belarusian hit nine double faults in the match, but with the Italian also firing eight, she was still able to win the match 6-4 6-3.
"We played each other four times before, so I knew how she plays - she doesn't make mistakes," Govortsova told the WTA website.
"I knew I had to be aggressive against her, and I did a good job of that today.
"I like clay. You can use volleys and slice more. I'm going to play more on clay this year, I didn't play much on it last year."
Second seed Julia Goerges had no such problems though as she defeated Aravane Rezai 6-4 6-0.
"Aravane's tough - she was top 20 before," Goerges said.
"You have to be ready for every ball when you play her and that's what I did. Not everything worked perfectly for me but you always work on fixing those things for your next match. And there were a few good things today. I'm happy I'm through."