The Swiss third seed won 7-6(7) 6-3 6-4 on a sunny Court Suzanne Lenglen and is now on a six-match winning streak on clay, having warmed-up for Roland Garros by winning the title in Geneva last week.
Progress was by no means straightforward against a skilful opponent ranked 93rd in the world and Wawrinka has yet to switch to his A game. But he says it's there when he needs it.
"If you look at the first two matches, for sure I'm not playing my best tennis, but I know I have my best tennis in me," the 31-year-old Wawrinka, playing in his 45th consecutive grand slam tournament, told reporters.
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"I'm happy to get through in three sets. For sure there were some ups and downs, it could have been better, but in general I think it's been a good day."
Twice a grand slam champion, Wawrinka needed five sets to scrape past Lukas Rosol in the opening round and found himself in trouble in the first set against Daniel when he trailed 4-6 in the tiebreaker.
The danger was averted with a sledgehammer groundstroke winner followed by consecutive aces, and he wrapped up the set with an angled smash.
Kitted out again in a dazzling fluorescent yellow shirt, Wawrinka controlled the second set but was a break down in the third before finishing with a flourish to secure a third round clash against French 30th seed Jeremy Chardy.
"Mentally I'm right there," Wawrinka, who beat top-ranked Novak Djokovic in last year's final, said.
"I always try to win in three sets. But at the end of the day... I do whatever I can to move on to the next round."
(Reporting by Martyn Herman; editing by Ken Ferris and John Stonestreet)
