Seven-times grand-slam champion Williams, who returned to the tour in March after dropping out with Sjogren's Syndrome, a fatigue-inducing autoimmune disease, looked to be struggling early in the match but found the resources to win.
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.
Asked how she was coping with her illness, a subdued Williams gave a deep sigh.
"My perspective changes every week," she told a news conference. "I just want to do my best and not be overwhelmed.
"It is definitely an adventure and a journey, and it is just life happening. I already know I can play (tennis), that is not a doubt...everything else is just up in the air."
Williams said she took inspiration from sister Serena and hoped to play doubles with her at the London Olympics in July and August.
"A lot of it I have to figure it out," she said of the illness. "It's physical and emotional and all kinds of different things, mental. So it's just something that you can only get if you live it. So I have to learn to laugh sometimes.
"Sometimes I wonder if it's something that I'm doing: did I do something wrong? Then I snap out of that pretty quick nowadays. But sometimes I wonder if this is my fault."
The former world number one could now meet third-seeded Pole Agnieszka Radwanska, who plays Serbian Bojana Jovanovski on Monday.