Goals from Guinea international Sambegou Bangoura and Paul Gallagher secured the Potters' fourth consecutive victory over Crewe.
But the future of manager Johan Boskamp remains unclear after an uneasy truce was broken with assistant Jan De Koning and director of football John Rudge.
Crewe hit back deep in stoppage time through substitute Eddie Johnson but it was too little too late.
The visitors should have been a couple of goals in front before they opened the scoring, but Luke Chadwick spurned a good opening when he volleyed straight at Ben Williams and the keeper rescued his side again when he beat away Darel Russell's shot from the bottom corner.
But Bangoura edged Stoke in front when he flicked on former Crewe captain Dave Brammer's flighted ball in the 16th minute.
The Alex came close to hitting back almost immediately but Steve Foster shinned a Kenny Lunt free-kick against the far post and the centre-half also missed a header after David Vaughan had planted the ball right at him with a pin-point free-kick.
Russell and Bangoura had more chances for the visitors before the break and a Bangoura header at the start of the second half had to be flicked from underneath the crossbar by Williams.
Stoke had taken a grip of the game and came close to a second when Bangoura and Mamady Sidibe failed to turn the ball home amid a goalmouth melee.
Gallagher wrapped things up in the 89th minute when he wafted an exquisite side-footer from left of the area into the far corner.
Although Johnson turned in Steve Jones' cross in stoppage time, Stoke had already claimed the victory.