Kamara, playing in his first game since returning from a loan to Norwich City of the English Premier League, got a pass from Claudio Bieler just outside the area and scored from that distance in the 68th minute.
Kansas City (6-4-4) emerged with the tie after team members successfully lobbied referee Drew Fischer to rescind a penalty kick awarded to Houston in the 38th minute.
Brad Davis scored in first-half stoppage time and goalkeeper Tally Hall made two spectacular saves for the Dynamo (6-4-3).
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