But Shrewsbury were vastly improved in the second half and began clawing their way back with their first shot on target, a wonderful rising shot into the far corner from James Bolton.
Shrewsbury were level in the 77th minute after Stoke’s Sam Clucas fouled Laurent in the area. Fejiri Okenabirhie’s penalty was clinical.
The comeback was complete four minutes later after more suspect Stoke defending, with Laurent unmarked to slide the ball in from four yards.
Stoke (4-3-1-2): Federici; Bauer, Williams, Martin Indi, Tymon; Etebo, Adam (Afobe 82), Clucas; Ince; Campbell (McClean 72), Crouch.
Substitutes: Haugaard (g), Berahino, Edwards, Souttar, Woods.
Booked: Etebo, Adam.
Shrewsbury (4-5-1): Arnold; Bolton, Waterfall, Sadler, Haynes; Gilliead (Angol 90), Laurent, Grant, Docherty, Okenabirhie (Eisa 88); Amadi-Holloway (Beckles half-time).
Substitutes: Agius (g), Emmanuel, Sears, Rowland.