Dallas got first-half goals from Jeff Cunningham and Dave van den Bergh and seemed in control of the match at the break. Movsisyan came off the bench in the second half and scored in the 54th minute to give Salt Lake a spark.
Robbie Findley then tied it in the 60th minute on a penalty kick. An own goal in the 88th minute by Daniel Torres gave Salt Lake the lead and Movsisyan scored again in stoppage time.
Salt Lake climbed to 6-7-5 and remained in sixth place in the Western Conference, one point behind Colorado. FC Dallas (4-9-5) trails Salt Lake by six points.