Milton Rodriguez and Marvin Chavez also scored for Dallas (12-2-13).
The victory also extended Dallas's unbeaten streak to 18 games, tying it for the league record. Dallas is in the playoffs for the first time in three years.
Cunningham got his 11th goal of the season in the second half. It tied him with D.C. United's Jaime Moreno for the all-time lead.
The Fire (7-11-8) are still mathematically alive in the playoff race, but have to win their last four matches to have any chance of qualifying.