Stoke have now lost five of their last seven matches, conceding 17 goals in the process, and find themselves two points above the dropzone having played two games more than 18th-placed West Ham United.
A wayward shot from Christian Atsu after seven minutes helped to kickstart the match, and the Ghanaian winger was involved again soon after when curling one wide.
Outcast midfielder Adam was proving to be Stoke's best player, coming close with another long-range effort and then sending in a fizzing cross that Darlow had to deal with.
Having had a penalty appeal rejected three minutes beforehand, the Spanish forward turned the ball past Butland following some impressive work by Murphy down the right-hand side.
Stoke, winners against Newcastle in their last four encounters here, applied some late pressure and came close to levelling things up.
Mame Biram Diouf was twice denied by fine Darlow saves, before shooting wide from close range and then glancing the ball over the bar in added time to potentially bring down the curtain on Hughes's tenure.
Stoke City (3-4-3): Butland; Edwards, Zouma, Wimmer; Cameron, Allen, Adam, Pieters (Berahino 71'); Shaqiri (Diouf 57'), Crouch, Choupo-Moting
Newcastle United (4-2-3-1): Darlow; Yedlin, Clark, Lascelles, Manquillo; Diame, Shelvey; Ritchie, Atsu (Gayle 64'), J.Murphy (Dummett 82'); Perez (Hayden 90')