The game featured only five shots, three by Chicago. FC Dallas garnered the only shot in the second half.
Dallas (2-2-6, 12 points) went ahead when Ferreira scored unassisted in the sixth minute. Ferreira and Fire defender Wilman Conde ran side by side to chase down a long looping ball, but Conde fell.
Ferreira then dribbled around him near the top corner of the box. Fire defender C.J. Brown charged over but ran past Ferreira, who sidestepped him and had a clear look at the top left corner past goalkeeper Andrew Dykstra.
The tying goal was scored when Justin Mapp used a full-leg kick to send the ball from near midfield into the box. McBride got behind defender George John for position and made a crisp header past goalkeeper Kevin Hartman.
The Fire's best chance to score in the second half came in the five minutes of stoppage time. A corner kick reached the far post, where Baggio Husidic and Dasan Robinson each got a foot on the ball while Hartman was out of position. Neither could get a clear shot on goal.
The Fire, who failed to score in two international friendlies last week, has a four-game winless streak in MLS play.