Johnson & Johnson persuaded a jury to reject a woman’s claims that the company’s iconic baby powder is laced with cancer-causing asbestos in its first trial win in New Jersey litigation over the product.

Jurors in New Brunswick, N.J., deliberated less than a day before unanimously rebuffing Rosalind Henry’s claims J&J sold its baby powder knowing it was tainted with asbestos, a carcinogen, said Carol Goodrich, a company spokeswoman. The ruling follows two mistrials in California where jurors couldn’t...