C.J. Sapong got Kansas off to a superb start after just ten minutes when he reacted quickest to slam home a rebound after hitting the post with a header.
Federico Higuain came closest to restoring parity in the first half with a long-range free kick, which was well saved by Jimmy Nielsen.
Jairo Arrieta spurned a series of chances to extend the lead for table-topping Kansas, and they were made to pay for those missed opportunities.
Ten minutes from time veteran midfielder Eddie Gaven headed a pinpoint cross from Emilio Renteria past Nielsen to level the scores.
An important late point keeps Crew within touching distance of Houston Dynamo and New York Red Bulls in the fight for the final playoff places in the Western Conference.
All three sides are separated by four points with just two games left in the regular season.