Prince - Purple Rain (release year 1984)
Like Radiohead's album, at least Purple Rain got nominated. The album that won in 1985 (because, again, the Grammys are weird about the timeframe from which albums are nominated) was Can't Slow Down by Lionel Richie. This made sense in Grammy minds as Richie appeared to be such a safer choice than the more rebellious Prince. Of course, as things turned out, Prince was pretty much a saint to whoever got to know him and Richie had some embarrassing - and very public - marital problems.
Of course, that last bit should have nothing to do with anyone weighing the merit of albums, but the Grammys, like the Oscars, are very much about appearance as much as truly taking a look at the quality of the work. There is nothing wrong with Richie's album, I guess, but groundbreaking it was not. 40 years later, very few people are listening to what Richie did while Prince is still an important figure in music, nearly a decade after his death.
Purple Rain, of course, also served as the soundtrack to the movie of the same name. While the album names Prince and the Revolution, we know the real truth. Prince wrote all the songs and likely played every instrument you hear on the record and recorded and produced the album as well. Purple Rain was a work of a musical genius just coming into his own.
Any album that begins with a track like "Let's Go Crazy" and ends with "Purple Rain" is almost definitely going to be one of the best pieces of music you will ever hear. Prince also used electronics in a different way than most records at the time, but he molded them in a way to augment the organic creation of the track. Every single track is a winner. This album remains a must-listen even today.