Bullets from high-powered rifles killed Ciara Lee, 24, a state corrections officer, and her son Devin Franklin, 2, The Miami Herald reported.
None of the six people in the home were the intended targets of the gunmen, police said.
"Two innocent people were shot doing the most innocent thing: sleeping," Cmdr. Delrish Moss, a Miami police spokesman, said.
One of the four other relatives inside the home received minor injuries.
Police said they think the gunmen were probably chasing someone who they mistakenly believed ran into the home and opened fire on every window in the house.
Police and the family of the victims were asking the public for assistance.
"I know for a fact that there's a lot of people in our community that know who these people are," Homicide Sgt. Ervens Ford said. "I'm willing to bet there's dozens of individuals that live among us in our community that call themselves human beings that know who these individuals are."
Ray Liotta sues skin care company over use of likeness
Boston schools pull out free condoms over wrapping complaints