Feilhaber should have doubled his side's advantage as he beat two defenders to raid into the box, but he could only put his effort wide of the target.
Roger Espinoza carved out another opportunity for the hosts as he weaved his way down the flank and picked out Nemeth in the box. The striker turned his man, but his shot went inches past the post.
Just before the break, Dallas were reduced to 10 men when Zach Loyd was given a second yellow card for a poor challenge on Nemeth.
In the second half, Kansas City capitalised on their numerical advantage when Nemeth found the run of Feilhaber in the box, who dispatched the ball past Dan Kennedy.
The home side notched their third goal of the game when Zusi lifted a dangerous corner from the right and Ellis rose highest in the box to power a header into the net.
Sporting sealed their victory in the 64th minute as Connor Hallisey raided through the middle and backheeled the ball into the path of Zusi, who slotted it past Kennedy.
Saad Abdul-Salaam almost added a fifth goal in the dying minutes when he lined up an effort from 25 yards, but his strike was well saved by Kennedy who kept the scoreline down for the visitors.