The pair had never met before and it was level pegging until the middle of the seventh game when Buzarnescu was serving for parity at 4-4.
Facing two break points, her second double fault of the encounter coughed up the break to give Williams the chance to serve for the opener at 5-3 after 29 minutes.
The 39-year-old American wrapped it up three minutes later with some assured groundstrokes from the baseline.
Williams had two chances to take the Romanian's serve at the start of the second set but Buzarnescu held firm.
Fight
The fightback appeared to embolden her hitting as errors crept into the Williams game.
Nevertheless, Williams carved out two more opportunities to break at 2-2 but could not convert.
She then lost her serve as Buzarnescu moved her around the court more convincingly. But Wiliams broke back immediately and levelled at 4-4.
It was tense trench warfare. And Buzarnescu dug herself out when facing two break points at 5-5 forcing forehand errors off Williams who then had to serve a second time to stay in the set. She failed.
Buzarnescu's fifth double fault gave Williams the break at the start of the decider and she went 2-0 ahead after saving two break points. While not demonstrably playing much better, the veteran American was soon 4-0 up.
Buzarnescu got on the board at 4-1 to maintain hope of a Williams implosion. It looked like it was coming while an increasingly tentative Williams was trying to take a 5-1 lead. But Buzarnescu fluffed two makeable forehands and Williams maintained her cushion.
It ended soon after. A 6-1 scoreline in the decider belied the overall endeavour of the two-hour struggle.
"I knew it wasn't going to be easy," said Williams. "She has a great service and I'm happy to get through it. It was good competition."
Elsewhere in the bottom half of the women's draw, there was a surprise as the 10th seed Belinda Bencic lost to the unseeded Russian Daria Kasatkina.
Former world number one Victoria Azarenka advanced to the third round with a 7-5, 6-4 win over the Danish teenager Clara Tauson and there was misery for the partisans as Caroline Garcia slumped to a straight sets defeat to Polona Hercog from Slovenia.
