The world number one is bidding to win only her second singles title at Roland Garros, 11 years after her first.
Her record on the Paris clay is at odds with her performance at the other grand slams. She is a five-time champion both at Wimbledon and the Australian Open, and has also won the US Open on four occasions.
Yet Williams has reached only one semi-final in the French capital since her victory over sister Venus in the 2002 title match, losing earlier or not entering in every other year. Twelve months ago she suffered a stunning first-round defeat to Virginie Razzano.
The red clay may not be her favourite surface but it was hard to detect a weakness on Friday.
Cirstea got to the quarter-finals four years ago, her best result in a grand slam, but the world number 30 had little answer to Williams as the 31-year-old American swept to a 6-0 6-2 victory in just over an hour on court.
One of the most dominant periods of her career has come since Williams began working with French coach Patrick Mouratoglou, who she hooked up with after losing early in Paris last year.
She said: "I didn't know it would be this successful. I honestly just thought I just needed a place to hit, and I'm an open individual.
"I'm open to a lot of different things, and I liked some of his suggestions, so it was just like we can try to work together and see how it goes.
\"I actually don't think about it, and after every match I'm reminded. And, ironically enough, I forget about it as soon as it's done.
"I don't think it's about a winning streak. I think it's about winning important matches and winning the right matches at the right time."
Having dropped just one game to Georgian Anna Tatishvili in the first round, and three to France's Caroline Garcia in the second round, it was routine again for Williams.
She was awaiting the winner of Saturday's third-round tussle between Czech Petra Cetkovska and Italian 15th seed Roberta Vinci.