While Kenin recovered from a tough start to reach round three, second seed Pliskova crashed out at the hands of 2017 Roland Garros winner Jelena Ostapenko.
Kenin – the fourth seed at Roland Garros – won nine of the closing 11 games to overcome Bogdan in a little under two hours on Court Philippe-Chatrier.
The pair previously met in 2018 in the final round of qualifying for the Rogers Cup. Kenin has gone from strength to strength since then but found herself behind after dropping serve twice in the first set.
The world number six bounced back in style, however, winning six break points in total as she went on to claim victory in the decider.
"During the match I just try to put the emotions aside," Kenin said in a post-match news conference. "I don't have time to think about my emotions. I have to play one point at a time.
"These two matches have been quite tough. I felt like I couldn't find my rhythm in both of them and found a way at the end, so I'll take it."
Kenin will go up against another Romanian in round three in the form of qualifier Irina Bara, with Alison Van Uytvanck having retired hurt.
There was little sign of further upsets in the day's second-round action, however, with Kenin joined in the next stage by Petra Kvitova, Aryna Sabalenka and Garbine Muguruza.