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.
"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)
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