Much of what remained of the house had smoke and water damage.
Three pets died in the blaze, according to family members.
Fire Department Battalion Chief Chris Petree said the family would not be able to remain in the house. He added the American Red Cross was called in to help the family.
Residing at the house were Marcos A. and Graciela Ochoa, their 13-year-old son and 8-year-old daughter. They were renting the house. Cousins also were staying in the house, according to fire officials.
Graciela Ochoa, according to her son, was shopping when the fire erupted. Marcos Ochoa was at work in Yuma. Their son added he was playing video games when he heard a popping noise from the back of the house.
He said he first thought someone was trying to break into the house, but he quickly discovered the fire. The boy said everyone got out of the house and went to a neighbor's home to call for help.
Fire officials determined that two youths at the house, thought to be ages 16 and 17, decided to smoke a cigarette. They didn't have matches, so they reportedly lighted a paper towel on the stove and then went outside, using the paper towel to ignite the cigarette.
The teens then dropped the paper towel into a bundle of clothes, Petree said.
Fire officials are calling the blaze an accidental fire.
Monday's fire came two weeks after the Ochoas were affected by a fire at 714 Brighton Ave.
That was the home in which Graciela Ochoa's mother, Maria Hoyos, resided before that house was destroyed by a blaze being investigated as an arson.
Family members said Monday Hoyos remains in a coma and has been transferred from El Centro Regional Medical Center to a San Diego hospital.
The investigation into that fire is ongoing, and there have been no arrests in that case.
>> Staff Writer Darren Simon can be reached at 337-4082.