The top-ranked Nadal trailed 5-1 in the third set before forcing the tiebreak.
"Probably, I am playing a little bit nervous," Nadal said. "And that's why (my) legs didn't work as well as usual."
Andujar said he thinks Nadal is "going through perhaps a period of doubt."
"I am not playing that well," said Nadal, who has spent 7 hours, 19 minutes on court. "I am not happy, but I am here."
Murray, who is still looking for his first Grand Slam after losing in three finals, beat Simone Bolelli of Italy 7-6 (3), 6-4, 7-5.
The fifth-seeded Soderling beat Spanish qualifier Albert Ramos 6-3, 6-4, 6-4.
"A win in straight sets is always good," the Swede said.
Fish reached the third round for the first time by beating Robin Haase of the Netherlands 7-6 (1), 6-2, 6-1, while No. 24 Sam Querrey of the United States lost to Ivan Ljubicic of Croatia 7-6 (2), 6-4, 6-4.
Fish, of Tampa, Fla., is seeded 10th at Roland Garros, making him the top American in the field. It's also his highest seeding at any Grand Slam tournament. Fish is the last U.S. man still in the tournament.
Fish saved the only break point he faced, while accumulating 17 break points against Haase and converting five.
The 29-year-old Fish lost his opening match in three of five previous trips to Paris.
Haase, who's ranked 54th, is 5-9 in Grand Slam matches.
Querrey arrived at Roland Garros this year with an 0-4 record in the Grand Slam tournament but won his first-round match against Philipp Kohlschreiber.
Ljubicic, a French Open semifinalist in 2006, hit four of his 11 aces in the first-set tiebreak.
In other results, No. 16 Fernando Verdasco of Spain and No. 18 Gilles Simon of France won, but No. 20 Florian Mayer of Germany, No. 27 Marcos Baghdatis of Cyprus and No. 32 Kevin Anderson of South Africa lost.
Information from The Associated Press was used in this report.