Williams' overtime gamewinner in the 109th minute came on a 15-yard shot after receiving a pass from Cunningham, who had opened the scoring with a penalty kick in 12th minute. The penalty kick was awarded for a foul on Freddy Adu by Wizards keeper Kevin Hartman.
With two minutes left in regulation time, Sasha Victorine equalized for Kansas City by slamming home a rebound from a Will John header.
The win sends Real Salt Lake against the Colorado Rapids April 28.
In the other U.S. Open qualifier between teams that did make the MLS playoffs in 2006, Columbus meets Los Angeles April 24 for a chance to face the New York Red Bulls. The two winners of the qualifying series join the top six 2006 MLS finishers in the round of 16 of the Open Cup proper.