I wouldn't call it a reinvention, but I've always liked Zac Brown Band's cover of Marshall Tucker's "Can't You See." I saw them (ZBB) a few years ago at Nats Stadium. Each one of the band members threw down a face melting solo. I'd always thought Can't You See was a little repetitive, but these guys sure changed my mind that night. I've wanted to find a professional recording of their long play cover but I've never seen one. Here's a semi-decent version on YouTube though:
Maybe not classic rock, but definitely primal rock and roll.
Forgot to say, The Cramps have (or rather had) reinvented a vast number of obscure early rockabilly and garage rock songs including Psychotic Reaction (originally by The Count Five), Surfin' Bird (originally by The Trashmen) and She Said (originally by the late, great Hasil Adkins).