Djokovic survives wobble to ease past error-prone Nadal in Paris as Swiatek cruises
His counterpart in the women's draw, world number one Iga Swiatek of Poland had an even easier morning, crushing France's Diane Parry 6-1, 6-1 to book her own third-round spot.
While Djokovic remains in the hunt for his elusive Olympic gold, Spain's Nadal now has only the doubles competition left to add to his two Olympic gold medals, partnering Carlos Alcaraz.
Djokovic led 6-1 4-0 before a Nadal comeback attempt that saw him briefly level 4-4.
"I was just very proud to be part of this match and ... I wanted to do my job on the court and really execute the game plan as much as I possibly can," Djokovic said.
"So almost a perfect match, the 6-1 4-0. Then things got complicated, I started to hesitate a little bit on my shot he stepped in, the crowd got involved and for all, it was really anybody's set, anybody's game.
"Just very glad to overcome this incredible challenge."
Alcaraz was also in action in the singles but was never seriously pressured in his 6-1, 7-6 victory over Dutch opponent Tallon Griekspoor. Eighth-seed Stefanos Tsitsipas punched his ticket for the next round, with the Greek finding even less resistance in his 6-1, 6-2 victory over Britain's Daniel Evans.
Sixth seed Casper Ruud of Norway was made to work harder in his three-set win over Italy's Andrea Vavassori.
In the women's draw Swiatek was joined in the next round by Czech Barbora Krejcikova, the new Wimbledon champion, who advanced with a straight sets victory over China's Wang Xinyu as did American Coco Gauff, beating Argentine Maria Lourdes Carle 6-1, 6-1.
Follow the women's singles at the Games here.
But all eyes on Monday were on the Nadal-Djokovic showdown with the crowd desperate to see the world's best claycourt player make one last run in Paris even though his best playing days are long behind him.
"I was not able to put him in difficult positions," Nadal said. "I was not able to have enough quality shots, enough quality of movements.
"Playing against Novak without creating damage to him and without having the legs of 20 years ago is almost impossible."
At age 37, Djokovic, who has won 24 Grand Slam singles titles to Nadal's 22, has remained far more competitive than his injury-plagued opponent. He left nothing to chance in a flawless display over a set and a half.
The world number two stretched the Spaniard with punishing groundstrokes and perfect drop shots, making him look his age as he raced through the first set and went 4-0 up in the second.
The crowd, ready for a mouth-watering epic on their record-extending 60th encounter, instead were being treated to what looked like a fast-track Djokovic win.
Nadal, with his thigh strapped due to a recent injury, was spilling unforced errors across Court Philippe Chatrier, lacking precision and consistency.
With the crowd sensing the end of an era was fast approaching, Nadal was desperate to avoid one of the most bruising defeats of his career on his favourite clay surface.
A Djokovic double fault saw Nadal pull back to 4-2 and that was celebrated like a victory with almost the entire stadium jumping from their seats to cheer him on.
After another two games, the Spaniard was level but it was nothing more than a brief reprieve as Djokovic sealed victory on his first match point with an ace.