Booing could be heard after the match as Kostyuk refused to shake hands with her opponent, having said beforehand that she would not shake hands with Russian and Belarusian players due to Moscow's invasion of Ukraine.
Sabalenka, who appeared to sarcastically bow to the crowd following the win, said she initially thought the boos were aimed at her.
"It was a very tough match, I mean tough emotionally. I'm sorry guys, I didn't get it at first, I thought this booing was against me so I was a little surprised," she said.
"But then I felt your support, so thank you so much."
The world No.2 had previously said she had nothing against Ukrainian people and felt bad for them as Moscow's invasion rages on. Belarus has been a staging ground for Russia's actions.
Sabalenka appeared in trouble on her serve early on and fell behind 2-3, but the unseeded Kostyuk could not build on her advantage and the Australian Open champion struck back immediately with a powerful crosscourt volley on break point.
Second seed Sabalenka wrapped up the first set in style in front of a sparse Court Philippe Chatrier crowd before pouncing in the next with an early break and another to go up 4-1, as Kostyuk wilted under the Paris sun.
The Belarusian raised her level again late in the match to save two break points and close out the victory in 71 minutes.
