Shaqiri put the visitors ahead with a brilliant strike after 26 minutes, cutting in from the wing before unleashing a dipping shot into the top corner.
The Swiss midfielder doubled the lead with a curling free kick five minutes after halftime to lift Stoke out of the bottom three.
Hull offered little in attack and slumped to their fifth league defeat in a row.
(Reporting by Ed Osmond, editing by Pritha Sarkar)
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