The blaze was reported about 5:30 p.m. in the 2500 block of N. Hancock Street.
The fire forced the family to the balcony of their second-story apartment. A man used a rope to lower a 5-year-old boy to safety, followed by that boy's 4-year-old cousin. Firefighters arrived shortly after that with a ladder to help to rescue an 8-year-old girl, her mother and that man.
Neighbors who heard the family scream rushed over to help.
"I see a family in the porch saying 'Help me, help me,'" said Miguel Ojeda, who tossed the rope up to the family.
It took 55 firefighters 24 minutes to knock down the flames, which were not visible from the building's exterior but generated a lot of smoke.
The fire is believed to have started in a storage room on the second floor, though the exact cause was under investigation.
Four units suffered water and smoke damage. Most residents were able to return to their apartment. The American Red Cross helped families displaced by the fire.