Brek Shea continued his fine form by scoring the opening goal in the 58th minute, while Jackson doubled the advantage in the 76th before the Crew’s Andy Iro was sent off in the final 10 minutes.
Dallas has now won its last three games to move closer to the Western Conference leading Los Angeles Galaxy, while the Crew had a modest two-game winning streak snapped.
The first half saw both sides struggle to create chances, with the best opportunity falling to Marvin Chavez for Dallas in the 31st minute when his left-footed effort was tipped off the post by Crew goalkeeper Will Hesmer.
Shea went close with a curling effort from the top of the penalty area in the 56th, but he opened the scoring two minutes later when Chavez had a low shot saved by Hesmer, with Shea following up the play and knocking home the rebound.
Jackson then doubled the lead in the 76th minute when he latched onto a through ball from Andrew Jacobson and flipped it over the shoulder of the onrushing Hesmer.
The result was then secure in the 83rd when Iro received a second yellow card for a foul on Chavez.
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