Nadal, a 17-time Grand Slam champion, cruised to a 6-2 6-1 6-3 victory on the rebuilt Court Philippe Chatrier to set up a clash with another German qualifier -- world number 114 Yannick Maden -- in round two.
Nadal had suffered three consecutive semi-final defeats earlier in the clay-court season, but appeared to find his best in an Italian Open title success sealed with victory over old rival Djokovic, while his French Open win-loss record now reads 87-2.
"It's always amazing to play here, the new Chatrier is very nice," the second seed said. "It's been an important place in my career. "I played a good tournament in Rome which was very important for my confidence. Now we'll see."
The 32-year-old Nadal raced into a 3-0 lead in the opening set before a second break of serve in the eighth game sealed it after just 40 minutes.
The second set was over in a flash as Nadal crushed nine winners past his beleaguered opponent.
The winning line honed into view when Nadal broke after a lengthy game to take a 2-1 advantage in the third, and the Spaniard completed the job on his first match point as world number 184 Hanfmann blasted long.
- Djokovic impresses -
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Djokovic laid down an early marker in his bid to hold all four Grand Slam titles simultaneously for the second time, powering past Polish youngster Hubert Hurkacz.
The 15-time major champion impressed in a 6-4 6-2 6-2 triumph and will face Swiss lucky loser Henri Laaksonen in round two.
"I was very solid. I'm happy with my game today," said the top seed.
"It's a long tournament... But I just want to concentrate on my next match." Twelve months ago, Djokovic dropped out of the world's top 20 after a shock quarter-final loss to Marco Cecchinato and even pondered skipping Wimbledon, but he has instead reclaimed his place at the top of the game.
The 22-year-old Hurkacz, who has claimed three wins over top-10 players this season, had no answer to the 2016 French Open winner, as Djokovic sealed a second-round spot without breaking sweat, hitting 27 winners.
Later in the day, 23-time women's major champion Serena Williams takes on Russia's Vitalia Diatchenko.