The attacker then turned his attention to a 32-year-old woman jogging farther south along the path, which winds through plantings, benches and public sculptures. She was stabbed in the neck.

“He continues to move south and a little east when he encounters a man with a stroller with his 2-year-old son,” Mr. Kelly said. “He slashes that man in the chest as the man is attempting to protect his son, and his son is slashed on the arm.”

The police declined to identify any of the victims, but the father was identified by colleagues as James L. Fayette, a former solo dancer with the New York City Ballet who now is a representative for the union that represents the dancers, the American Guild of Musical Artists. His son, Luke, was released from a hospital after receiving several stitches, but Mr. Fayette remained in serious condition on Tuesday evening.

As the attacks mounted, it quickly became clear that the normally peaceful park had been transformed into a scene of violence.

A bystander who saw the father being attacked confronted Mr. Graham, the police said, and was able to wrestle him to the ground, keeping him subdued until the police arrived at 8:04 a.m.

“He did a good job,” Mr. Kelly said.

The bystander, who declined to give his name before being whisked away by police officers, told reporters that the real hero was the father.