Eddie Vedder covering NIN's "Hurt," but using Johnny Cash's arrangement, is an example. PJ's cover of "All Along the Watchtower" is also based much more closely on the Hendrix version than on Dylan's original, as many covers of "Watchtower" are (including many of Dylan's own performances).
Here's one non-PJ example that springs to mind: Leonard Cohen's original "Hallelujah" was released in 1984. John Cale covered it in a solo piano version on a 1991 tribute album. Rufus Wainwright's cover from the Shrek soundtrack in 2001 seems very clearly based on Cale's version rather than Cohen's (Jeff Buckley's version from 1994 is a different thing entirely, but also leans closer to Cale's style than to Cohen's).
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