Harry Duke hit an impressive 106 from just 55 balls to set the tone for a commanding batting performance by Yorkshire. James Wharton and George Hill registered 73 and 63 respectively, while Matt Revis chipped in with 49.
Yorkshire racked up a colossal 382 runs as Shropshire could only collect five wickets in the process.
George Hargrave top-scored for Shropshire with 40, but they were ultimately unable to make up the deficit as they fell significantly short.
Peter Clark also scored 29 for Shropshire, but they were bowled out for 135 inside 32.5 overs as Dom Bess took four wickets and Revis and Dominic Leech took two each.