The Crew took the lead in the 78th minute on a goal by Bernardo Anor, but two critical referee decisions allowed Los Angeles to escape with the win.
Andy Gruenebaum was called for a foul in the 85th minute on Jose Villareal in the penalty area and Keane made good on the kick.
Anor was then whistled for another foul during stoppage time against Keane and the Galaxy striker again took advantage of the opportunity.
Los Angeles improved to 8-7-3 and won for the second time in three games. Columbus fell to 5-8-5.