Lancemc
Blue Crack Addict
The only other time I remember it happening in film was with The English Patient, and during the Oscars I was rooting for Fargo. A subsequent second viewing of TEP made me realize I was dead wrong, and it's the only piece of media in my personal Top 10 that was a top award winner.
I'd say No Country is probably the closest a Best Picture winner comes for me in recent years. Certainly in my top 5 of that year still. Before that it has to go back to An American In Paris. Closest the Grammy's have come are probably Time Out of Mind then The Joshua Tree before that.