Keane scored off Stefan Ishizaki's cross, racing into the goalmouth to volley past goalkeeper David Ousted for his third goal of the season.
The Galaxy improved to 2-1-1 with their second straight victory.
Vancouver (2-2-2), which will be home against Los Angeles next weekend, had three strong scoring opportunities in the first half, but struggled in the second half.
''I thought going into halftime (Vancouver was) going to hit the wall a little bit in the second half,'' Galaxy coach Bruce Arena said. ''They worked real hard the first 45 minutes, had to chase the ball a lot, and they were going to lose some of that energy in the second half, and certainly getting the goal early changes the game.''
Galaxy goalkeeper Jaime Penedo made three big first-half saves, turning aside Darren Mattocks' shots in the 20th and 32nd minutes and denying Kekuta Manneh 1-on-1 just before halftime.
''The boys played very well,'' Whitecaps coach Carl Robinson said. ''Obviously, one minute of lack of concentration in the start of the second half cost us. A long straight ball, the ball got in behind us and Robbie finished off. Disappointed with the goal, but very pleased with the performance.''
Los Angeles' best first-half chance was an eighth-minute drive by Keane at Whitecaps goalkeeper David Ousted. Keane maneuvered through open space in Vancouver's box to finish the cross from Ishizaki, who beat Jay DeMerit on the right edge of the area to send the pass to the far post.
''A great play by Stefan on the goal, taking that ball down, getting it by DeMerit and whipping in a great cross to Robbie Keane,'' Arena said. ''A great play.''
There were several chances to add to the lead, but Landon Donovan fired sharply at Ousted two minutes after Keane's goal. Second-half substitute Rob Friend fired just wide of the left post on an 82nd-minute breakaway, and Keane chipped over the crossbar in a 1-on-1 situation in the 88th.