Juan Pablo Garcia scored the other goal for Chivas, who remain in fourth place in the Western Conference with 30 points.
After Garcia scored in the 77th minute, Chris Rolfe scored the equalizer with his fourth goal of the season.
When Fire defender took down Jonathan Bornstein in the 90th minute, Suarez put the penalty kick in the goal.
The Fire have lost four straight matches.
Celebrity Couples of 2014 [PHOTOS]