Reis made the save on former Rev Benny Feilhaber after the ball came loose in the penalty area, to preserve the scoreless tie for New England (1-1-1).
Jimmy Nielsen wasn't tested with a direct shot on net for Kansas City (1-1-2), which has yet to notch a victory since a season-opening win over Philadelphia.
SKC had 13 attempts on goal to New England's three.
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