Cops nabbed a guy they say pulled the home invasion that forced Magic Johnson's daughter to run for her life.
Law enforcement sources tell TMZ ... LAPD identified the suspect after reviewing surveillance video from the neighborhood where Elisa Johnson's friends were renting a house back in December.
We broke the story ... 2 armed men got inside the home and started terrorizing Elisa's friends, holding them at gunpoint and making off with a Rolex, cash and electronics. She was able to escape out of a sliding glass door at the back of the home.