The showdown between the two most successful men's tennis players in history appeared to be fizzling out before a late fightback from Nadal enabled him to avoid his heaviest-ever defeat by Djokovic.
"I'm very relieved," said Djokovic. "Everything was going my way, I was 6-1, 4-0 up but I played a sloppy service game and gave him chances."
It was 24-time Grand Slam champion Djokovic's 31st win in a rivalry that began on the same Roland Garros clay courts in 2006.
The Serb added: "I never thought back in 2006 that we'd still be playing each other almost 20 years later."
Nadal admitted Djokovic was the "clear favourite" ahead of their first clash in more than two years, with the Spaniard a shadow of the player who reigned for the best part of two decades at Roland Garros.
While 14 of Nadal's 22 Grand Slams have come in Paris, the 38-year-old has been plagued by injuries in recent years and he has slumped to 161st in the world.
His participation in the singles in Paris had been in doubt until the last minute.
Djokovic has not had a good season by his stratospherically high standards but the 37-year-old Serbian rose to the occasion in his pursuit of an elusive Olympic gold.
The top seed raced into a 5-0 lead before Nadal finally got on the board but Djokovic closed out the set and surged 4-0 ahead in the second before Nadal offered some belated resistance.
Nadal clawed his way back to 4-4 only for Djokovic to break once more, this time making no mistake as he put away his old foe and perhaps brought down the curtain on one of the greatest rivalries in the history of the sport.
Djokovic, a bronze medallist on his Olympic debut in 2008, goes on to face Matteo Arnaldi or Dominik Koepfer for a spot in the quarter-finals.
Nadal will turn his focus to the doubles where he is in a dream-team pairing with compatriot Carlos Alcaraz.
Alcaraz, the reigning men's French Open and Wimbledon champion, takes on Dutchman Tallon Griekspoor later Monday in the singles.
Unstoppable Swiatek
Women's world number one Iga Swiatek stepped up her quest for gold by powering into the third round.
The four-time French Open champion underlined her status at the heavy favourite in Paris, swatting home hope Diane Parry aside 6-1, 6-1 and will meet China's Wang Xiyu for a place in the quarter-finals.
The Pole has won her past 23 matches at Roland Garros, with three clay titles already under her belt this season.
Swiatek, tested in her opening match under the roof on Court Philippe Chatrier, enjoyed a far more straightforward outing in bright sunshine on Monday.
"I think it was a pretty solid performance, better than the first round, so I'm happy that I could play a little bit more of my game and, of course, the conditions were also nice," she said.
US second seed Coco Gauff dispatched Argentina's Maria Lourdes Carle 6-1, 6-1.
Next up for her is Wimbledon semi-finalist Donna Vekic, who put out former US Open champion Bianca Andreescu.
Italy's Jasmine Paolini, this year's French Open runner-up to Swiatek, eased into the third round with a 6-4, 6-1 victory over Magda Linette.
Wimbledon champion Barbora Krejcikova coasted past China's Wang Xinyu while Maria Sakkari of Greece also advanced.
Scorching heat posed a considerable problem for players at the Tokyo Olympics, and the issue could resurface this week with highs of 35 degrees Celsius (95 degrees Fahrenheit) expected on Tuesday.
