Three-time Roland Garros champion Williams, who has been stuck on 23 major titles since 2017, one behind Margaret Court’s all-time record, went through the gears in the opening set before letting her guard down.
The 39-year-old, who is seeded seventh in Paris but has not been past the fourth round here since reaching the final in 2016, fell 4-2 behind in the second set as Buzarnescu broke for the first time.
But the American was back to her dominant self as she stole her opponent’s serve in the next game and set up two break points in the 11th game.
Buzarnescu kept her composure to stave them off and level for 5-5 before sealing the second set on Williams’s serve.
Williams was 4-0 up after breaking twice in the decider but the scoreline did not reflect the fight the Romanian put up to stay in the contest.
Williams’s experience, however, prevailed in the key moments as she set up a meeting with fellow American Danielle Collins.
Williams has come agonisingly close to matching Court’s record since winning the 2017 Australian Open.
She has fallen in four Grand Slam finals and earlier this year lost in the semi-finals at the Australian Open.
Following that she underwent oral surgery and played only three Tour-level matches heading into the French Open, winning one. (Reporting by Julien Pretot; Editing by Toby Davis)