The Hoops showed too little, too late as Chicago won to take control of a vital playoff spot and keep Schellas Hyndman out of the postseason.
Chicago took the lead in the 25th minute, as Mike Magee's corner was headed in by Juan Luis Anangono. Magee "scored" his team's second a few minutes before the interval, when Alex's effort deflected off the forward's face to give him a 19th goal of the year, tying him for the MLS Golden Boot lead.
Jalil Anibaba scored a spectacular third for the visitors in the 52st minute, turning to unleash a 25-yard dive to flew across the fact of the goal and beat Chris Seitz.
Dallas pulled one back in the 63rd minute. David Ferreira whipped in a cross and Kenny Cooper used his strength to hold off Gonzalo Segares, turn and put a shot past Sean Johnson for his fifth goal of the season.
Cooper scored a second in the 75th minute. Jackson and Segares became entangled in the box, and Dallas was awarded a penalty by referee Kevin Stott. Cooper stepped up and put his shot right down the middle to bring the Hoops within a goal.
Chicago (13-12-7) goes to fifth in the East with the win, tied with fourth-place Montreal and sixth-place Philadelphia on 46 points but ahead of the Union via the wins tiebreaker. Dallas (10-11-11) is mathematically eliminated from the playoffs with two games remaining.