The loss put the Fire on the verge of missing the playoffs. They can still match New York and Houston with 43 points by winning their last two starts. Chicago would still be behind on the goal differential tiebreaker.
Dallas controlled the flow of the game from the start, and the pressure paid off with Jackson's goal in the 41st minute. He took a long pass from Ugo Ihemelu, beat Fire defender Jalil Anibaba and left-footed a low shot past goalkeeper Sean Johnson.
Cruz made it 2-0 in the 53rd minute, putting a bicycle kick past Johnson. That became the game-winner when Chicago's Sebastian Grazzini beat Dallas keeper Kevin Hartman with a curling 16-yard shot in the 86th minute.