The world number one, who turned 35 on Sunday, converted eight of 18 break points against Nishioka under the roof on Court Philippe Chatrier on a rain-interrupted day.
"I have to be pleased overall. I always expect highest from myself, so I can always do better, but was a very good start of the tournament," added Djokovic.
He will next meet either Federico Coria of Argentina or Slovakia's Alex Molcan, who is working with Marian Vajda -- Djokovic's former long-time coach.
Nadal, on a quarter-final collision course with Djokovic, brushed Australia's Jordan Thompson aside 6-2, 6-2, 6-2 to improve his Roland Garros record to 106 wins and just three losses since his 2005 title-winning debut.
"It's a good start, of course, straight sets," said Nadal, seeded fifth.
"I played good for a while. Then things that I could do better and I need to do better. But it's a positive start."
The Spaniard, who last week downplayed concerns over the recurrence of a foot injury that plagued him in Rome, meets Corentin Moutet in round two after the French wildcard defeated 2015 champion Stan Wawrinka.
Osaka, Krejcikova dumped out
Four-time Grand Slam winner Osaka was knocked out 7-5, 6-4 by Amanda Anisimova -- the same player who ended the Japanese star's title defence at the Australian Open this year.
Osaka served eight double faults and committed 29 unforced errors on her return to Roland Garros, after withdrawing in 2021 when she refused to honour mandatory media commitments before revealing she had been suffering from depression.
"I thought I tried really hard, and I just feel like it was a bit unfortunate because I wasn't able to play as many matches leading into this tournament," said Osaka, unseeded at a Grand Slam for the first time since the 2018 Australian Open.
Anisimova, the 27th seed, reached the semi-finals in Paris three years ago.
"It's tough to see Naomi Osaka in the first round so I knew it wouldn't be easy," said the American.
"I knew I had to play my best tennis and the conditions were not easy."
Women's defending champion Barbora Krejcikova also crashed out, losing 1-6, 6-2, 6-3 to 19-year-old Diane Parry of France in her first match since February following injury.
The Czech world number two had yet to play on clay this season after being sidelined by an elbow problem.
"I just think I just collapsed physically, and, I mean, it was tough because I didn't play the matches," said Krejcikova.
Fifth seeded Anett Kontaveit became the fourth top-10 player to fall before the end of the second day, going down 7-6 (7/5), 7-5 to Australia's Ajla Tomljanovic.
Iga Swiatek, the favourite for the women's title, stretched her winning streak to 29 matches by dispatching Ukrainian qualifier Lesia Tsurenko 6-2, 6-0 in 54 minutes.
The 20-year-old Swiatek, who took over as world number one following Ashleigh Barty's shock retirement, has won her last five tournaments and is bidding for a second French Open in three attempts.
"Today was a pretty good match," said Swiatek.
She is unbeaten since February and has the longest winning streak on the WTA tour since Serena Williams won 34 matches in a row in 2013.
"I'm pretty sure that it can end, but I just want to keep going. I'm sure someday my streak will stop."
Ten matches were interrupted due to rain and will resume on Tuesday.