The Estonian, who had a first-round bye, was broken once in the first set and twice in the second in her first match on grass for almost a year.
"I remember last year when I played in (qualifying) here, it was much easier for me in the main draw," said Kanepi, whose No. 17 world ranking is more than 200 places higher than Rodionova's.
"I think I didn't have any rhythm at all and she played very well. I didn't move her around and it's pretty difficult to have a 'Plan B' on grass if your game's not working," she said.
"I am very impressed and very happy that I can get a win like this," Lucic said. "Sometimes when you start the grass-court season you have to prepare your mind as well as your body. You have to stay positive, and I felt like I did that."
Lucic made the Wimbledon semifinals in 1999 as a promising 17-year-old but was absent from the WTA Tour for much of the last decade because of personal problems. After spending several years on the lower-tier ITF circuit, she is back in the top 100 for the first time since 2000.