Jankovic, a semi-finalist here in 2006, landed 69 percent of her first serves and had only two double faults to set up a third round match against Frenchwoman Alize Cornet.
Third-ranked Jankovic had never played Govortsova and admitted she had trouble figuring out her shots.
She said, however, her form had improved from her 6-2 7-6 victory over Slovakian Jarmila Gajdosova to open the tournament.
"It was a lot better than my first round," said Jankovic, who had only 12 unforced errors against Govortsova. "But I feel also a little bit slow, especially on the returns.
"And not knowing the way how (Govortsova) plays, sometimes she comes up with very hard shots, very deep, and then all of a sudden there are some other shots that I don't really expect.
"So I was trying to focus and just really try to watch the ball carefully because my reactions, especially on the return, were not really that great.
"I was trying to get in a rhythm and just feel the ball and just play the game. But obviously I am just improving and getting better and better and just getting in form."
Jankovic described her memories of her semi-final run a year ago as "amazing".
"If I look at myself, I felt like I was flying on the court." she said.
"I was just so fast. I look at myself now, it's totally different player, different girl.
"But I feel more mature, more experienced. I'm having a lot of fun. I'm just enjoying my game."