The 46-year-old former world number one was unable to halt her losing run against the 23-year-old Stoiana, who secured victory in straight sets to advance to the second round.
Williams struggled to find her rhythm during the opening set and fell 5-2 behind after stumbling while chasing a return. Despite receiving strong support from the crowd, the seven-time Grand Slam singles champion could not turn the contest around.
Stoiana maintained her composure in the second set, winning 6-3 to complete the victory and condemn Williams to another early singles exit.
The defeat extends Williams' losing streak to 17 matches. Her last victory in a WTA Tour singles match came in July 2025, when she defeated Peyton Stearns at the Washington Open.
Williams also suffered a first-round defeat at the Guangzhou Open last week, losing to Austrian teenager Lilli Tagger. However, she enjoyed a better run in the doubles competition in Guangzhou, reaching the semi-finals alongside Indonesia's Janice Tjen.
Following Monday's defeat, Williams was asked about her plans for the 2027 season and said she had not made any decisions about her future.
"I haven't made any plans for next year, but I didn't make plans this year either. I just took it one step at a time. We'll see," she said.
The American also joked that she might ask her younger sister, Serena Williams, about her plans and follow her lead.
Stoiana will now face either Romanian top seed Sorana Cirstea or Maria Timofeeva in the second round.
Despite the latest setback, Williams remains one of the most decorated players in women's tennis history, having won seven Grand Slam singles titles and reached the world number one ranking during her illustrious career.