World number two Nadal, making a late start to his claycourt campaign after a foot injury hit his schedule, looked a bit rusty but did enough to register his 37th consecutive win on clay.
Clement, who overcame Nadal in the semi-finals of the Marseille Open in February before taking the title, troubled his opponent with an early break in the second set.
Spaniard Nadal then had his right ankle strapped before he fought back to level the set. He broke the Frenchman in the ninth game to serve for the match.
The French Open champion earned two match points and wasted the first before Clement hit a crosscourt backhand wide to bow out after 95 minutes.
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"The injury is no longer a problem."
"It was my first game on clay this season and I was a bit nervous. I did not play very well but this is normal."
He will meet Jean-Rene Lisnard in the second round after the unfancied Monaco resident beat British teenager Andy Murray 4-6, 7-6, 7-5.
SAFIN OUT
Argentine sixth seed and 2004 champion Guillermo Coria started his pursuit of a fourth consecutive final appearance in the principality with a 6-3, 6-1 victory over Russia's Mikhail Youzhny.
He will next meet Frenchman Paul-Henri Mathieu, who knocked out Russian Marat Safin.
Former world number one Safin, struggling to recapture his best form after a seven-month injury layoff, slumped to a 6-0, 7-5 defeat.
Safin lost the first eight games and needed 44 minutes to hold serve for the first time.
"I had fever last night and had to take a lot of pills. It took a lot of energy from me," said Safin.
Spaniard Carlos Moya, who won the tournament and the French Open in 1998, ran out of steam in a 6-3, 3-6, 6-1 defeat by Chilean Fernando Gonzalez.
Frenchman Sebastien Grosjean, seeded 13th, beat Spaniard Fernando Verdasco 7-6, 6-3.
(Writing by Patrick Vignal and Julien Pretot in Paris)