Martins' goal in the 30th minute when he got possession of the ball 35 yards from goal, dribbled in a few feet and then fired a volley past goalkeeper Jimmy Nielsen for a 1-0 Montreal lead.
Kansas City missed on second-half tries by Matt Besler and Kei Kamara, then fell behind by two in the 63rd minute when Bernier scored on a penalty kick for the Impact (3-5-2).
Eastern Conference-leading Sporting (7-2-0) dropped its second straight after opening the season with seven consecutive victories.
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