The visitors could have taken the lead in the 21st minute when Deshorn Brown was played behind the Kansas defence and he tried to loop a header over Jimmy Nielsen only to see the keeper collect the ball with ease.
Just before half time, Brown had another good chance to find the net as Dillon Powers found him on the edge of the area. He struck his shot well but Nielsen made an excellent save to tip the ball over the bar.
From the resulting corner, Hendry Thomas rose highest in the penalty area and headed at goal but his effort crashed off the crossbar and City managed to scramble the ball away.
The game looked to be heading for a draw but in the 88th minute Kansas found a winner through Graham Zusi volleyed into the net after being teed up by CJ Sapong's header across goal.