New England scored the first and last goals of the game after Juan Agudelo beat two defenders and sent a shot past the oncoming goalkeeper in the 11th minute. Scott Caldwell angled home Charlie Davies' back-pass in the 64th.
The game swung when Sporting KC scored three first-half goals in 14 minutes.
Dominic Dwyer equalized it at 1-1 in the 29th minute by rolling in a left-footed shot after settling a cross with his chest.
Nemeth's glancing header of Benny Feilhaber's free kick gave Sporting KC a 2-1 lead in the 39th. Four minutes later, Feilhaber converted a penalty after New England was called for a questionable foul in the penalty area.
Nemeth made it 4-1 in the opening minute of the second half when Jacob Peterson won the ball deep in New England territory and fed a cross to an unmarked Nemeth.
Sporting KC had not played since May 9 because its match against Colorado was postponed last weekend. New England had its nine-game undefeated streak snapped.
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