The sixth-seeded Stosur, a Roland Garros runner-up in 2010, needed just over an hour to see off the world number 68 in front of a sparce crowd on Court Philippe Chatrier.
Stosur ran into a spot of bother when Baltacha broke back in the ninth game but she upped the pace and won the remaining seven games, ending her opponent's ordeal with a return winner.
"It's nice to be on a real clay court again and actually feel like you can play more clay court tennis," Stosur said, referring to the controversial blue clay at this year’s Madrid tournament.
"I think that's one of the things that's probably annoyed a lot of people is that you're on a clay court but you can't play real clay court tennis.”
However Laura Robson has been handed a place in the draw as a lucky loser.
The 18-year-old lost her final qualifying-round match but will play Spain's Anabel Medina Garrigues after Silvia Soler-Espinosa pulled out.
Heather Watson and Anne Keothavong are also in the draw and face Elena Vesnina and Melinda Czink respectively.
For Williams, who returned to the tennis tour in March after being diagnosed with a fatigue-inducing blood disorder, her tortuous 4-6 6-1 6-3 win over 120th-ranked Argentine
The winner of seven grand slams, including five Wimbledon titles, struggled to hold her own serve as Ormaechea, 19, refused to go quietly.
Williams found some of her old strength of mind to break the Argentine to love in the ninth game of the deciding set and take the victory, but her next task could be a hard one - she could face third-seeded Pole Agnieska Radwanska who plays lowly Serbian Bojana Jovanovski on Monday.
"She played beautifully," Williams said of Ormaechea, who grew up idolising the Williams sisters. "I was mostly hoping that my experience would help me out."
The American former world number one could now meet third-seeded Pole Agnieszka Radwanska, who plays Serbian Bojana Jovanovski on Monday.
As the day cooled on Philippe Chatrier Court, both Williams and Ormaechea struggled to hold serve in the final set but the American gained the upper hand and, with some superb service returns, won the ninth game to love to take victory.
The Serbian, seeded 13th, finished off a 59-minute 6-1 6-1 demolition with an ace.