Huddersfield are in 14th position - three points clear of the dropzone - but head coach David Wagner will be concerned with the Terriers having gone six games without a win in the top flight.
Chances were few and far between as the first half progressed past the half-hour mark, but Stoke should have taken the lead just before the break.
Xherdan Shaqiri was played in behind the Huddersfield defence but despite only having Jonas Lossl to beat, the Swiss winger wanted too much time to get a shot away and the goalkeeper eventually blocked his effort.
Shortly after the restart, Shaqiri had the ball in the net but his acrobatic strike was ruled out for offside, although it did not take the home side much longer to establish a deserved lead.
After being released down the left flank, Eric Maxim Choupo-Moting was able to pick out the run of Allen who was able to convert from inside the penalty area for just his second league goal of the season.
The home side were first to the majority of balls and they came close to doubling their advantage midway through the second half, only for Lossl to be equal to Shaqiri's strike after he had cut inside from the right.
Shortly afterwards, it was effectively game over as Biram Diouf found the net via the inside of the post after being teed up by neat work from Shaqiri and Choupo-Moting, who had initially regained possession.
Huddersfield had their own opportunities during the final quarter of the game, with Rajiv van La Parra seeing a half-volley kept out by Jack Butland and Colin Quaner glancing a header wide after meeting a set piece.
However, it was all too little too late from the Yorkshire side, who must now start to contemplate a relegation battle ahead of fixtures with Liverpool and Manchester United.
STOKE CITY (4-3-3): Butland; Bauer, Pieters, Zouma, Shawcross; Allen, Fletcher, Adam (Cameron 71'); Shaqiri, Choupo-Moting (Ramadan 94'), Diouf (Crouch 77')
HUDDERSFIELD TOWN (4-2-3-1): Lossl; Malone, Hadergjonaj, Schindler, Zanka; Hogg (Depoitre 79'), Mooy; Van La Parra, Ince (Quaner 56'), Pritchard (Sabiri 60'); Mounie