The home side almost started the game in perfect fashion but Kenny Cooper was denied by the post as he headed Zach Lloyd's cross at goal.
Dallas were again prevented from taking the lead by the woodwork when David Ferreira's free kick beat everybody in the penalty area and the ball clattered the post and then almost crossed the line, but Matt Besler cleared it away.
However, the game was to turn when C.J. Sapong was sent off in the 70th minute for kicking the ball at Andrew Jacobson, who was down on the pitch with an injury.
The home side began their comeback in the 87th minute when Jacobson headed Ramon Nunez's cross over Jimmy Nielsen into the net.
In the 90th minute, Dallas got their equaliser as Walker Zimmerman rose highest in the penalty area to head past Nielsen to earn his side a point.