Fourth seed Halep was in complete control against her Russian opponent on Tuesday as she raced to a 6-0 6-2 victory in less than an hour on court.
The Romanian has not had the best of times at Roland Garros in previous years, with only one second round appearance to her name in five attempts, but believes the nerves that affected her previously are now under control.
Kleybanova was no match for the world number four and Halep was on the verge of a double bagel when 6-0 5-0 up in the second set.
She was not able to achieve that, but left the court satisfied with her start to the second Grand Slam of the year.
“It was nice,” she said. “I had a good feeling and am glad I started the tournament so well.
“For first time in my career, I was pretty relaxed for the first round of a major and I’m happy that I could beat her in two sets.
“I think I did well today. And she’s a great player on clay.
“But today I felt really good and I had a good feeling at the ball and at my game. Now I need to keep focused for the next round.”
Halep will face Great Britain’s Heather Watson in the second round after she came past Barbora Zahlavova Strycova 6-3 6-4.
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