Claudio Bieler put Kansas City ahead 1-0 with a penalty kick in first-half stoppage time, but the Impact (8-2-2) responded after the break.
A poor clearing attempt led to Nyassi's equalizing tally in the 49th when his low shot through traffic beat from the edge of the area reached the net despite Kansas City's protests that he was offside.
Warner's decisive score came in the 53rd for the Impact, who took over first place in the Eastern Conference with the victory.
Sporting (6-5-4), meanwhile, remained winless in three matches.
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