Leonardo Ulloa bagged his third of the campaign to help the newly-promoted Foxes record their first top-flight win in 10 years.
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Stoke started the brighter of the sides and Steven N'Zonzi fashioned their first shot, surging from his own half before slicing his effort wide of the post.
The Foxes were reduced to trying their luck from range by virtue of Stoke's solid defence, as Andy King watched his 30-yard strike sail just over the bar.
Crouch missed another chance to fire the Potters ahead after performing an acrobatic effort to strike Glenn Whelan's cross wide before half time.
Nigel Pearson's side weathered even more pressure from the hosts in the second half, before Ulloa hit the Staffordshire side with a sucker punch after the hour mark.
The Argentine, a club-record £8m signing in the summer, continued to vindicate Leicester's decision to recruit him by tapping home Paul Konchesky's far-post cross on 65 minutes.
Hamer produced late heroics on his Premier League debut and denied Mame Biram Diouf twice in the space of 10 seconds toward the end to preserve his side's lead.