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Scholze attributes the tilting construction for perfectoid rings to Fontaine, who calls it "a classical construction in $p$-adic Hodge theory".

Would anyone happen to know an early reference where one can see this construction being used to good effect? Are there canonical examples of classic applications?

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    $\begingroup$ I suggest that you read Fontaine's Bourbaki seminar on perfectoid spaces. $\endgroup$
    – Laurent Berger
    Commented Oct 3, 2019 at 11:27

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Jean-Marc Fontaine Groupes p-divisibles sur les corps locaux. Astérisque 47-48, Soc. Math. France, Paris (1977), i+262 pp (especially chapter V)

This is probably the canonical answer to your question. Note that the application was found before tilting was defined, even for fields, as is usually the case in the history of mathematics.

Jean-Marc Fontaine and Jean-Pierre Wintenberger. *Le "corps des normes'' de certaines extensions algébriques de corps locaux, C. R. Acad. Sci. Paris Sér. A-B 288 (1979), 367-370

Jean-Marc Fontaine and Jean-Pierre Wintenberger. Extensions algébrique et corps des normes des extensions APF des corps locaux. C. R. Acad. Sci. Paris Sér. A-B, 288(8) :A441–A444, 1979.

Jean-Pierre Wintenberger. Le corps des normes de certaines extensions infinies de corps locaux ; applications. Ann. Sci. École Norm. Sup. (4), 16(1) :59–89, 1983.

Two mathematicians that are sorely missed.

For a more recent application (still much older than perfectoids), see for instance

Christophe Breuil Une application du corps des normes. Compositio Math. 117, 1999, 189-203

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