Chicago, which advanced to the MLS semifinals for the third time in four seasons, limited the Burn to one goal and won the series, 2-0-1.
The Fire, 9-0 in playoff games at Soldier Field, will face the Galaxy in the best-of-three semifinals, beginning Oct. 10.
Kovalenko opened the scoring in the 17th minute, and Armas, who returned from injuries and a commitment to the U.S. national team, slipped a shot past Burn goalkeeper Matt Jordan in the 55th minute.
Miami 2, Kansas City 1-Chris Henderson scored the tiebreaker in the 71st minute at Ft. Lauderdale, Fla., in the third game of a quarterfinal series.
The victory gave the Fusion, the No. 1 seed in the playoffs, six points in the first-to-five-points series. Miami advanced to the semifinals against the San Jose Earthquakes, beginning Oct. 10.
Former Wizard midfielder Preki pulled Miami even, 1-1, on a direct kick in the 14th minute, less than 30 seconds after the Wizards took a 1-0 lead on Onandi Lowe's goal.