Dallas which was held scoreless for the first time since June 6 against San Jose.
Jason Johnson found a streaking Accam for a right-footer from just outside the box to open the scoring in the 4th minute.
Chicago's Matt Watson was shown a red card in the 78th minute but Dallas' Kellyn Acosta was penalized in the area about 7 minutes later and Maloney's kick to the bottom-left corner gave a Fire a 2-0 lead.
In San Jose, Diego Valeri sent a penalty careening off the crossbar in the 75th minute as the Portland Timbers settled for scoreless draw with the San Jose Earthquakes in the day's only other match.
The single point for the draw moved the Timbers past Seattle into fifth place in the Western Conference.
Both teams came into the match looking to end winless streaks. San Jose avoided losing its fifth straight match and the Timbers are winless in their last four, all on the road.