The former FA Cup champions are now perched on top of Championship log with 81 points four rounds of matches to go. They are a point above West Brom and six clear of Brentford in third and need just seven points to guarantee their return to the top flight.
Mateusz Klich put the victors on the scoreboard through a penalty shortly before the break. elder Costa, Liam Cooper, Pablo Hernandez and Patrick Bamford scored one goal apiece to complete the rout.
The loss sees Stoke drop to 21st on the table, just a point and a place above the relegation zone.
Leeds travel to seventh place Swansea as Stoke welcome Birmingham City as the promotion and relegation race becomes hotter. Both matches will be played on Sunday at 4.30 pm.