Roared on by a crowd fuelled with optimism following the appointment of Paul Lambert as the replacement for sacked manager Mark Hughes, Stoke started brightly but they had to wait until the second half for the overdue celebrations to begin.
for the goals to come as Joe Allen and then Mame Diouf got their names on the scoresheet.
Charlie Adam set Eric Maxim Choupo-Moting free down the left and his cut back was steered into the bottom corner of the net by Allen after 53 minutes.
It got worse for Town when, after Xherdan Shaqiri brought two decent saves from Jonas Lossl before a lovely flick set up Diouf for the second goal in the 69th minute, the Senegalese sliding a shot into the net off the inside of a post.
Huddersfield offered very little as an attacking threat and are now without a win in six Premier League matches, a run which has seen them slip to within three points of the relegation zone.
“It was difficult today,” said Wagner afterwards. “They were able to take the atmosphere from the stands, Stoke and their supporters were really on it.
“We were not able to create chances but it shouldn’t be a surprise as Stoke are a top quality side and they showed that with the second goal with the one-touch football they played.
“I have to accept where we are in the table. It’s only us who can change it.”