Czech Pliskova, who will next play either Germany's Laura Siegemund or American wildcard Coco Vandeweghe, made up for a wayward first serve by painting the tramlines for outright winners or forcing Mladenovic into errors.
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While the first set lasted only 25 minutes the 26-year-old Mladenovic stepped up her game in the second, the Frenchwoman moving Pliskova around the court more.
Highlights of Pliskova's victory over Mladenovic
But the Czech's serve improved and after a wobble when she was broken for the first time she took the last three games and clinched the match in one hour, 24 minutes.
"I think it was quite good for first match," Pliskova told reporters. "Of course the match was not easy. So I think, yeah, it was a good test for a first round."
"I think it starts always with me," said the Czech. "If I play good and fast enough, deep enough, then there is not much she can do.
"So it was ... mainly about me, because I thought if I can just play good tennis, I think I'm going to be fine, which I kind of was."