Peterson tallied in the 6th minute, barely staying onside after receiving a pass from Peterson Joseph, splitting the defense and beating goalkeeper Andy Gruenebaum.
Bunbury added an insurance goal in the 82nd minute for Kansas City (11-5-3), which moved three points ahead of D.C. United atop the Eastern Conference with 36 points.
Columbus (6-7-4), meanwhile, fell for the third time in four contests.
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