Kenin, who had lost her opening matches in both Dubai and Doha in recent weeks, made it consecutive wins in Lyon as she scraped through 6-7 (5/7), 7-5, 6-4.
The fifth-ranked American was on the brink of defeat as Romania's Cristian had match point on her serve at 5-4. Kenin rallied to break her opponent and then forced a third set.
The top seed failed to serve out victory while leading 5-3 in the decider but sealed her place in the next round with a break in the following game.
"Obviously I didn't feel my game that well - I was pretty frustrated the whole match, I couldn't find my rhythm, but I just tried to fight through," Kenin told the WTA website. "I got the win - it's a relief and I'm happy."
Kenin, 21, will next meet France's Oceane Dodin, who received a walkover against Jil Teichmann of Switzerland.
Second seed Kristina Mladenovic crashed out in the second round after a 6-3, 6-3 loss to Germany's Anna-Lena Friedsam.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ