After a goalless opening 45 minutes, Charlie Adam's floated pass found Eric Maxim Choupo-Moting, who cut back for Allen to finish.
Stoke doubled their lead on 69 minutes, when a sublime flick from Xherdan Shaqiri fell into the path of Diouf, who slotted beyond Jonas Lossl.
A first win in five matches moves Stoke out of the bottom three, in 17th place on 23 points. Huddersfield are one point and three places further ahead.
Stoke: 31 Jan v Watford (H)
Huddersfield: 30 Jan v Liverpool (H)