A 21-year-old man allegedly beat his month-old daughter to death and murdered her mother with a machete before setting their Bronx apartment on fire, police sources said Friday.

Elgidio Lind was being grilled by detectives after firefighters found the bodies of his girlfriend, Louisa Rodriguez, 32, and their baby, Angela, stuffed under a smoldering mattress at her Kingsbridge pad Thursday night, the sources said.

Rodriguez, who was naked and stabbed multiple times, appeared to have died from a massive head wound, sources said.

The smoke eaters then found little Angela Rodriguez unconscious in an empty bathtub.

The baby girl died a short time later — despite the brave efforts of one firefighter who tried to breathe life into the child’s tiny lungs as he rushed her to an ambulance, captured in a Daily News photo.

An autopsy found Angela died of blunt force trauma, not smoke inhalation.

Neighbors said they often heard Rodriguez fighting with Lind, who has a dozen prior arrests that include robbery and assault.

Detectives noticed cuts to Lind’s hands when they found him hiding at a gal pal’s home Friday morning, sources said.

Charges were pending late Friday.