Bertens struggled with cramps as the final set developed, eventually sinking to the clay in relief and pain following her 7-6 (7-5), 3-6, 9-7 victory, which took three hours and 11 minutes.
"She leaves the court in a chair and now she's in the locker room and eating in the restaurant, perfect. She exaggerated. It made me very angry. So, well done to her, but she can win without doing that."
The Spaniard dropped just four games as he breezed past American Mackenzie McDonald to advance to the third round, winning 6-1, 6-0, 6-3.
It took Nadal just 35 minutes to win the first set and, after breaking McDonald's opening service game of the second set, he dominated the match.
The 34-year-old faced zero break points and hit only 15 unforced errors.
Nadal has won the French Open a record 12 times and has lost only two French Open matches since 2005.
The 19-time Grand Slam winner is aiming to lift the trophy for the fourth year in a row.
The world No. 2 will face Kei Nishikori or Italian Stefano Travaglia in the next round.