The Resolutes, of the Christian Brothers' college, defeated the Monarchs, of the St. Louis university, on last Thursday, by a score of twenty to three. The heavy batting of C. Jenks and J. Shockey were the features of the game.-St. Louis Globe-Democrat, May 16, 1886
I'm absolutely not an expert on 19th century college baseball so I'm not really sure that this game represents an actual college baseball game or just a game between clubs made up of college students. In fact, I don't know enough to state that that's even a distinction that should be made.
There were clubs in St. Louis made up of college students going back to the mid-1860's when both SLU and Washington University fielded clubs that, at least unofficially, represented their respective schools. The Union Club, of course, was made up largely of students from those two schools and was established in 1859 or early 1860. So college students were forming clubs and playing games twenty years before this particular game.