By picking up a point on the road, Kansas City (3-6-5) remained unbeaten in its last six contests.
Philadelphia (6-4-5) has gone four games without a victory but is still tied for first place in the Eastern Conference.
Philadelphia had the best scoring chances, one of them coming when striker Carlos Ruiz hit the crossbar on a header in the 72nd minute. Nielsen's save of Mapp's shot came 5 minutes later.
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