Barrett scores injury time winner to inch the Galaxy closer to the Supporters' Shield.
Starting the match without David Beckham, Robbie Keane and Landon Donovan (the American came on in the second half), the Galaxy were able to stymie the Crew for 90 minutes, keeping them off the scoreboard at Crew Stadium.
Josh Saunders, who is still starting for the injured Donovan Ricketts made a number of key saves to keep the scores level. He was also assisted by defender Michael Stephens early in the second half who was able to clear the ball off the line to keep the match scoreless.
The breakthrough came late in second half stoppage time when Donovan was able to get off a powerful shot from the left of Will Hesmer's goal. The keeper parried it away forcefully but unfortunately for the Crew, it went right to Barrett who slotted it home calmly to give the Western Conference team the points.
Los Angeles improves to 5-0-1 in its last six matches and will now begin preparing for its CONCACAF Champions League group stage match with Mexican side Moreila on Wednesday. Columbus, which is no longer in first place in the Eastern Conference thanks to Houston's victory earlier in the day, will travel to LIVEStrong Sporting Park next weekend to take on Sporting Kansas City.