The Impact (9-11-5) had a pair of early scoring opportunities and another late in the match, but Donovan Ricketts, who finished with five saves for the Galaxy, used acrobatic saves and great positioning to thwart the Montreal attacks.
Ignacio Piatti found Justin Mapp on a break, but his left-footer toward the far post was poked away by the right hand of a diving Ricketts in the first minute.
About 6 minutes later, Piatti split four defenders a fired a shot from the top of the box but, once again, Ricketts dove a slapped it away. Andres Romero slammed home the rebound from the left flank, but was called offside.
The Galaxy (13-8-8) are winless, and scoreless, in their last two matches after averaging 4.3 goals per game during a four-game winning streak that ended with a 1-0 loss as San Jose on Aug. 28. Los Angeles sits a point behind first-place Vancouver in the Western Conference standings.