LAFC evened the score in the 57th minute on a corner kick that Impact defender Jukka Raitala inadvertently kicked into the goal while trying to clear it from the box.
Carlos Vela gave LAFC the lead in the 87th minute on a penalty kick and Latif Blessing capped the victory with a score in the 89th minute.
LAFC (4-0-2) will make its home debut on April 29 against the Seattle Sounders at 6 p.m.