Bieler tallied in the 5th minute, snapping a 197-minute scoring drought for Kansas City, and Zusi scored in the second half for an insurance goal.
Jimmy Nielsen posted a third shutout for SKC (2-1-2), which broke a three-game winless spell.
The Impact, meanwhile, fell to 4-1-0 following four consecutive victories to start the season.
Boston schools pull out free condoms over wrapping complaints
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