Mark Hughes' men had failed to string together consecutive top-flight wins this season before West Brom's visit and, although the away side will count themselves unlucky not to have earned a share of the spoils, Diouf's second-half double proved decisive.
Brown Ideye, Chris Brunt and Craig Gardner all went close for the visitors in a keenly contested first half, while the in-form Bojan Krkic showed flashes of his ability in attack for Stoke.
But the hosts appeared considerably more focused at the start of the second half and Diouf broke the deadlock six minutes after the break.
Gareth McAuley nearly drew West Brom level as he hit the post with 65 minutes on the clock and Stoke capitalised on that let-off, securing victory through a fortuitous Diouf goal shortly after, increasing the pressure on the visiting coach Alan Irvine.
Supporters were treated to a frenetic opening at the Britannia Stadium, though the home side took a little longer to settle despite Hughes making just the one change from Friday's 1-0 win at Everton – replacing Jonathan Walters with Peter Crouch.
Ideye, one of four brought in after the 3-1 defeat to Manchester City, wasted West Brom's first chance inside 60 seconds as he raced on to a long ball and blazed over the crossbar.
Stoke unsurprisingly began to look more dangerous going forward once Bojan started to get involved and the Spaniard almost put the hosts ahead in the 14th minute, sending an effort agonisingly wide of the bottom-left corner from 20 yards.
But West Brom remained threatening, with the evasive movement of Ideye and Stephane Sessegnon causing Stoke plenty of problems at the back.
And both were involved seven minutes before the break, as a fine West Brom move ended with Brunt blasting a fierce left-footed effort just off target from 30 yards, much to the relief of goalkeeper Asmir Begovic.
Stoke seemed to begin the second period with renewed urgency and Diouf opened the scoring in the 51st minute, slotting past Ben Foster after producing a clever first touch 12 yards from goal.
West Brom almost pulled one back through McAuley with 25 minutes to go, but the defender prodded against the woodwork amid a goalmouth scramble and Stoke made them pay just a few moments later.
Marko Arnautovic's wayward effort from outside the area struck Diouf, subsequently deceiving Foster, who could only watch as the ball rolled into the net.
West Brom desperately poured men forward during the final 15 minutes, but their attackers appeared bereft of ideas and Stoke ultimately cruised to the win, ending 2014 in victorious fashion.
