The Russian lost six games in a row during her first-round victory over Richel Hogenkamp and had to dig deep again to beat Donna Vekic in round two.
Serving for the first set at 5-3, Sharapova allowed the world number 52 from Croatia to break back before eventually getting over the line 7-5.
She dropped serve early in the second, and later served for the match at 5-3 again, with the same outcome.
However, Sharapova recovered to triumph 7-5 6-4 to keep her first Roland Garros campaign in three years on track.
This time last year Sharapova had recently returned from a 15-month doping ban, but she had not built her ranking high enough to qualify and was not offered a wild card.
But 12 months later Sharapova is back in the world’s top 30, seeded 28th at Roland Garros and a potential challenger for the title.
She will face Karolina Pliskova, the sixth seed, in the third round.
Wimbledon champion Garbine Muguruza, the 2016 Paris winner, had a more comfortable route into round three.
The Spaniard was rarely troubled in a 6-4 6-3 victory over French wild card Fiona Ferro to set up a meeting with Australia’s Sam Stosur.
“It’s always tricky when you face a young, talented French player,” said Muguruza. “It probably wasn’t the best tennis out there but I’m happy that I managed to fight and to win.”
Stosur knocked out 30th seed Anastasia Pavlyuchenkova of Russia.
