What particular anime first showcased crossovers?
It's probably as early as those old Go Nagai shows. There's a couple of movies where several of his franchises were together. To name a few:


Mazinger Z Vs. Devilman (1973)
Great Mazinger tai Getter Robo (1975)
Great Mazinger tai Getter Robo G (1975)
Grendizer - Getter Robo G - Great Mazinger Kessen! Daikaijuu (1976)
UFO Robo Grendizer tai Great Mazinger (1976)


Crossovers consisting of Devilman, Mazinger Z, Great Mazinger, Getter Robo, Getter Robo G, Grendizer, and UFO Robo Grendizer.

Also, Lupin III is by Monkey Punch and Detective Conan is by Gosho Aoyama. It was a planned collaboration. Both shows are produced by Tokyo Movie.