Top seed Djokovic, looking for a Roland Garros title to complete a career Grand Slam, claimed his 50th win at the tournament by seeing off Belgian qualifier Steve Darcis 7-5, 6-3, 6-4.
It was the Serb's third win in three career meetings with Darcis, a player nicknamed 'Shark' who dumped Nadal out of Wimbledon in 2013.
But it was a far from a smooth display from the 11-time major winner and three-time French Open runner-up who committed 42 unforced errors.
"He has a lot of talent and it was tough. I am happy to have won in three sets."
Djokovic next takes on Britain's Slovenian-born Aljaz Bedene who reached the third round of a major for the first time with a 7-6 (7/4), 6-3, 4-6, 5-7, 6-2 win over Spain's Pablo Carreno Busta.
Nine-time champion Nadal became just the eighth man to record up 200 Grand Slam match wins as he saw off Argentina's world number 99 -- and fellow left-hander -- Facundo Bagnis 6-3, 6-0, 6-3.
"The most important thing is a victory in the second round more than the 200 victories," said Nadal, who now has a 72-2 win-loss record at Roland Garros.
Roger Federer, missing from the French Open this year, tops the all-time list of Grand Slam matches won on 302.
Djokovic is sixth with 216 after his win on Thursday.
Top seed and defending women's champion Williams cruised into the last 32 with a 6-2, 6-1 win over Teliana Pereira of Brazil.
The 34-year-old American will next go up against either
France's Kristina Mladenovic or Timea Babos of Hungary.
Venus Williams was to follow her sister on Court Suzanne Lenglen against 20-year-old compatriot Louisa Chirico who came through qualifying.
Also reaching the third round on Thursday were 2010 semi-finalist Tomas Berdych, the seventh seeded Czech, who defeated Malek Jaziri of Tunisia 6-1, 2-6, 6-2, 6-4.
Latvia's Ernests Gulbis, who beat Federer on his way to the semi-finals in 2014, made the last-32 with a 6-2, 7-5, 6-3 win over Portugal's 26th seed Joao Sousa.
Germany's Alexander Zverev, the only other teenager left in the draw, made the last 32 of a major for the first time by beating 36-year-old Frenchman Stephane Robert 6-1, 3-6, 6-1, 6-4.
Serbian 14th seed Ana Ivanovic, the 2008 winner, defeated Japan's Kurumi Nara 7-5, 6-1.
Dutchwoman Kiki Bertens followed up her first round win over Australian Open champion Angelique Kerber by beating Camila Giorgi of Italy 6-4, 6-1.
Swiss eighth seed Timea Bacsinszky, a semi-finalist last year, defeated Canada's Eugenie Bouchard 6-4, 6-4.
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