Hughes, appointed at the end of May, had seen his charges lost 2-0 to Houston Dynamo in their tour opener but an improved display saw them deserve their victory.
Walter tucked home a low right-footed shot after 24 minutes when he was on the end of an intricate build-up on the fringe of the FC Dallas penalty area.
Stoke should have doubled their lead in the 82nd minute but substitute Cameron Jerome failed to convert a penalty as goalkeeper Raul Fernandez saved low down to his right.
The Premier League side lost defender Andy Wilkinson to a red card seconds later, as FC Dallas attempted to clear the ball away. Twenty-five yards out from goal, Wilkinson swung his left foot at the ball in the hope of connecting and testing Fernandez, but he missed his kick, and as he tried again he clattered late into Danny Garcia, resulting in the dismissal.