The 11-time champion at Roland Garros saved four break points in his first service game on Court Philippe Chatrier but was never troubled again by the 184th-ranked German, who was playing for the first time in the French Open main draw.
Nadal's feared forehand was not at its dangerous best, accounting for more unforced errors (11) than winners (nine).
Djokovic also needed under two hours to reach the second round, running his Grand Slam winning streak to 22 matches by getting past 44th-ranked Hubert Hurkacz of Poland 6-4, 6-2, 6-2.
Djokovic is attempting to become only the second man in history to hold all four major titles at the same time on two separate occasions. Rod Laver was the only player to achieve the feat when he won all four Grand Slams in 1962 and 1969.
Meanwhile, after throwing up twice on the court, Tiafoe said he was "very depleted'' for the fifth set. He said he didn't think he had food poisoning because he felt fine before the match.
"Throwing up during the match isn't something that normally happens to me ... I threw up again when I went to the locker room after the third set. The fifth-set result obviously came to that because (I) was obviously very depleted and had nothing really in me. It was tough to end like that," he said.
Tiafoe was coming off his best Grand Slam showing, a quarterfinal run at the Australian Open.
The Associated Press contributed to this report.