Moffat broke a 1-1 tie when he fired home a Brad Davis corner kick that eluded goalkeeper Kevin Hartman. The goal came 13 minutes after Dallas had been put a man down when Jair Benitez was handed a straight red card for elbowing Colin Clark.
Will Bruin scored in the 3rd minute for the Dynamo (5-4-4), who improved to 3-0-1 at BBVA Compass Stadium, which opened May 12, claiming the El Capitan rivalry trophy between the Texas teams.
Jackson found the net in the 59th for FCD (3-9-4), which extended its winless streak to 10, including seven losses.
2014: The Year in Fashion [PHOTOS]
LeBron James reveals his new Nike shoes