Galaxy took the lead in the 42nd minute, against the run of play, as Ashley Cole made a run into the box and hit a low cross that was turned in by Ola Kamara.
The lead appeared to be short lived, as Dave Romney turned the ball into his own net off the subsequent kickoff, but the own goal was chalked off as Gyasi Zardes was judged to have played the ball over the endline before the goal.
Zlatan Ibrahimovic was brought down in the Columbus box 10 minutes after halftime, and the Swede stepped up and buried the penalty kick.
Then Romain Alessandrini, who came off the bench to replace an injured Kamara, scored to give the Galaxy a three-goal lead, before he capped off the scoring with his second goal in second-half stoppage time.
Meanwhile, Boateng's compatriots Lalas Abubakar and Harrison Afful saw 90 minutes of action for Columbus Crew as Jonathan Mensah was absent.