Two couches with polyurethane pillows fueled the fire so it became hot enough to cause "flashover," a phenomenon where other objects in a room heat to the point of almost-explosive ignition, Battalion Chief John Walsh said.
"It happened while the occupants were still in the building," he said. "That's why they're extremely lucky."
Firefighters responded to the one-alarm blaze at about 5:55 a.m. at a two-bedroom, single-story unit at 16860 Meekland Ave., fire spokeswoman Aisha Knowles said.
Responding crews encountered thick smoke and flames pouring out of a front-facing window in the living room area, where an electrical problem appears to have sparked the blaze, Walsh said.
Neighbors woke up the family, and an adult son was able to leave through the back door, Knowles said.
The father jumped out a rear window as the mother went to the bedroom where their two young daughters were sleeping. She then handed the girls, ages 6 and 8, to the father through a window.
"Thankfully once all the family members got out of the house, they had a meeting place designated," Knowles said. "That's a fire safety lesson we try to teach families."
She said about half of the 800-square-foot unit -- including the kitchen and living room -- was engulfed in flames.
There was also significant heat damage to the other rooms, leaving the family's clothing unsalvageable, and the neighboring unit sustained light smoke damage.
The Red Cross was called to assist the family.
Three birds and a tank full of fish perished in the blaze.
Walsh said the family did have a working smoke detector, but the polyurethane couch cushions burned similar to gasoline.
The fire accelerated quickly and reached flashover, which happens when the radiated heat causes other objects to decompose and produce vapors that suddenly and violently ignite, Walsh said.
Flashover is extremely dangerous to firefighters, but in this case it happened before emergency crews had arrived.
Responding firefighters extinguished the blaze in about 10 minutes, Knowles said.
"We feel fortunate no one got hurt," Walsh added.