Nadal, who lost his first ever match at Roland Garros last year when he was defeated by Robin Soderling in the round of 16, extended his record to 32-1 on the Parisian clay on Tuesday.
"First day here is always a little bit more nervous than usual," Nadal said. "I think I played bad, but I won anyway, without problems, so that's always important."
Nadal committed 28 unforced errors and had to save nine break points against the 655th-ranked Mina. He said he remembers having what he considered spotty starts in the first round each of the four years he went on to win the title.
"I know I have to refocus and calm down and move forward," Nadal said. "I think I will have no problems."
Unbeaten on his favorite surface this season, Nadal has already won three titles on clay this year, at Monte Carlo, Rome and Madrid.
The match was Roddick's first on clay since he lost in the fourth round at Roland Garros last year.
"There was a lot of ugliness out there today," he said. "But, you know, at the end of it, I get to play again. You go into a day hoping to get through a day, and I got through today."
Seeded sixth, Roddick barely avoided losing his opening French Open match for the fifth time. Instead, he earned his first five-set win in the tournament since 2001, the first year he competed, when he beat Michael Chang in the second round.
U.S. men went 5-6 in the first round, an improvement on last year, when they went 2-7. Only four have reached the third round since 2006.
Their best hope for an extended stay this year is Roddick, even though his most recent tournament was more than seven weeks ago at Key Biscayne, where he won the title. He withdrew from this month's Madrid Masters because of illness.
"Spending three days in bed in Madrid wasn't the way we wrote it up," Roddick said. "That was bad. That was not the preparation we wanted."
Playing on center court for the first time since 2005, he looked rusty at times against Nieminen, a veteran left-hander from Finland. But Roddick's serve saved him -- he hit 19 aces and was broken only twice.
A knack for clutch play in tiebreaks helped, too. Roddick found himself only three points from defeat leading 5-4 in the breaker. But he hit a forehand chip for a winner and a booming forehand to take the set and even the match.
Roddick is 16-4 in tiebreaks this year.
His past three Grand Slam defeats have been five-setters, but this time he took charge approaching the finish. A lunging forehand slice helped him break to take the lead for good at 3-2, and a double fault by a weary Nieminen on match point gave Roddick the win.
"I've been saying all week if I can get through the first one or the second one, then maybe I will start hitting my stride and playing a little bit better," Roddick said. "But it's just a matter of surviving and advance."
The 98th-ranked Ginepri beat Querrey 4-6, 7-6 (3), 6-4, 6-2 to reach the second round at Roland Garros for only the second time in eight appearances at the clay-court Grand Slam tournament.
Ginepri, of Kennesaw, Ga., hadn't won a match on clay this season.
Querrey, of Santa Monica, Calif., had been playing well on clay, including winning a title this month in Belgrade, Serbia. But his career mark at the French Open is now 0-4.
"Not into it. Mentally not there. I mean, you know what? I don't know. Just did not enjoy myself out there. It's been like that on and off for, like, a while," Querrey said. "I don't want to be fighting myself out there and also fighting the opponent."
In other action, No. 7 Fernando Verdasco beat Igor Kunitsyn 6-4, 6-2, 6-2; ninth seed David Ferrer defeated David Guez 6-1, 6-3, 6-1; 16th-seeded former champion Juan Carlos Ferrero beat Pablo Cuevas 6-4, 6-3, 6-1; No. 22 Jurgen Melzer rolled past Dudi Sela 7-5, 6-2, 6-4; No. 28 Lleyton Hewitt defeated Jeremy Chardy 7-5, 6-0, 6-4; and No. 30 Philipp Kohlschreiber beat Karol Beck 7-6 (7), 6-1, 6-1. Unseeded Grega Zemlja upset No. 26 Juan Monaco 7-6 (6), 3-6, 7-5, 6-3.
Information from The Associated Press was used in this report.