"It might not have been "hard," but Larry appears to be the first person in the history of the Internet to publish such a finding. His conclusion: It was a June 5, 1985 game that the Cubs lost (of course they did) 4-2 to the Atlanta Braves. Go on over and please read Larry's post for more of his detective work.
That's not to say that there might not have been any movie magic at play here: SB Nation's Al Yellonpresents his case on why Matthew Broderick, Mia Sara and Alan Ruck likely shot their Wrigley scenes later in the year and the TV footage of the June 5 game was edited into the movie later.
As an aside, one of the minor things that always bugged me about "Bueller" — and about any movie shot in Chicago — is when they're driving along, say, Lake Shore Drive and then, in the next cut, they're going the opposite direction, only to switch back a second later. Not important to the movie; it's just art. It only matters to the synapses of a local who knows which way is which.
No such creative license was taken in filming the baseball scene, however. Featuring real players in a real game, it remains as pure as Bueller's intentions."