The three commerce pioneers set the pattern. Salesforce launched its web API on February 7, 2000 — the earliest of the three and generally credited as the first commercial web API. eBay followed in November 2000, opening its marketplace to third-party commerce tools. Amazon shipped its API in July 2002, which became the seed of everything that followed at that company.
Salesforce is the cleanest example of the whole model in miniature: expose the platform, let an ecosystem build on it, and turn that ecosystem into a durable business advantage. The AppExchange is the direct descendant of that decision.
But “first” deserves an asterisk. Machine-to-machine business integration long predates the web API. EDI was doing structured, automated commercial exchange between trading partners for decades before 2000, and RPC as a model goes back further still. What the 2000-era pioneers invented was not the idea of programmatic exchange — it was doing it over the open web, self-service, with documentation anyone could read.
That accessibility is the actual innovation, and it is worth remembering when someone claims the API economy is only fifteen years old. The economy is; the practice is much older.