The Sierra Leone international headed home Teal Bunbury's cross to put the hosts ahead on four minutes.
Moments later, Bunbury had to be substituted after sustaining an injury in a collision with Red Bulls midfielder Paulo Nagamura.
Things got worse for Kansas midway through the first half, as Kamara levelled the scores by putting through his own net.
The Eastern Conference leaders dominated the remainder of the match, but they were unable to produce the winning goal that their play deserved.
New York, who failed to record a single shot on target, remain two points behind Kansas in the standings.