The Whitecaps (7-3-4) lost Darren Mattocks to a pair of yellow cards in the 60th minute, but managed to hang on for the victory thanks to Le Toux's tally in the 80th.
Davide Chiumiento found the Vancouver striker with a cross-field feed on the game-winning play.
The Rapids (6-7-1) almost netted the equalizer 2 minutes later when Martin Rivero fired a shot off the upright following goalkeeper Martin Bonjour's sliding challenge on Edu.
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