Kamara put Kansas City ahead 1-0 in the 4th minute. On the play, Teal Bunbury chipped Graham Zusi's pass from midfield behind the defense as New York goalkeeper Bill Gaudette rushed up to make a play.
Kamara beat defender Connor Lade with a header into an empty net.
But he also scored an own-goal in the 28th minute when his attempt to head away Sebastien LeToux's free kick went into the Kansas City goal.
The draw broke a three-game winning streak for SKC (14-7-5), but allowed them to keep a two-point margin over New York (13-7-6) in the race for second place in the Eastern Conference.