The girl was abandoned at a parking lot at Firestone Boulevard and South Gate Avenue, across the street from a church carnival.
Police said a man and a woman were arguing, and the man approached a security guard, asking him to watch the girl for a moment. The man, whom the guard presumed was the father, said he'd be right back, but then disappeared.
The couple left in a white sedan, but never returned.
The mother and boyfriend came forward on Monday morning, saying it was a misunderstanding. Apparently, both thought the other was watching the child.
Police are not releasing the little girl's name.