Hughes saw his side lost 2-0 to Houston Dynamo in their opening game but they were much improved against a crowd of almost 10,000 in Dallas.
Republic of Ireland international Walters scored with a low right-footed shot after 24 minutes from the edge of the penalty area following a neat passing move.
Stoke should have doubled their advantage in the 82nd minute but substitute Cameron
Jerome failed to convert from the penalty as goalkeeper Raul Fernandez saved low to his right.
City had a man sent off shortly afterwards after defender Andy Wilkinson was red carded.
Wilkinson failed to connect with the ball as he attempted to clear upfield from 25 yards and after crashing into Danny Garcia with his second attempt, he was dismissed.
Stoke complete their tour of the US when they face Philadelphia Union on Tuesday.