Mark Hughes's men recorded their maiden victory while on tour, the Irishman netting a fine finish from Erik Pieters's pass as their MLS opposition were beaten in Texas
The Republic of Ireland international produced a classy finish midway through the first half after a slick pass from Erik Pieters to give the visitors their first victory on their tour of USA.
Substitute Cameron Jerome should have added to the tally from the penalty spot 15 minutes from full-time but his attempt was well saved by Dallas goalkeeper Raul Fernandez.
Stoke finished the game with 10 men after Andy Wilkinson was given his marching orders late in the contest for violent conduct.
Mark Hughes made four changes to the side who suffered a 2-0 loss to Houston Dynamo on Wednesday and the visitors dominated the early exchanges.
But it was the home side who created the first genuine chance when Mexican Michel caught Asmir Begovic off guard, forcing a desperate goal-line clearance from Pieters.
Begovic was called into action again when former Manchester United youngster Kenny Cooper fired on goal before Walters struck at the other end.
Pieters unleashed Walters with a delightful through-ball and the Irishman finished clinically for the only goal of the contest.
Hughes made five half-time changes but that did not upset the visitors' rhythm as they dominated the second half without adding to the scoreboard.