The 2005 Best Picture winner "Crash" was a huge upset, as most people anticipated the win would go to "Brokeback Mountain". Though this may be the biggest surprise Best Picture winner, it's certainly not the first.
I will give you the winner at the 2003 Oscar ceremony, and four choices, three of which were nominated in that category. You have to give me the choice that wasn't nominated.
According to the 'AFI's 100 Years... 100 Movies' list, some of the Best Picture Oscar winners are not the best movies of the year. Here are questions on that.