The first award it earned was the Best Foreign Language film, for Yojiro Takita's Okuribito (also known as “Departures”). This is the first time Japan has ever won in the category, although three Japanese films were accorded the honor when it was offered as a special/honorary award rather than a regular category. (Those films are: Akira Kurosawa's Rashomon, Teinosuke Kinugasa's Gate of Hell, and Hiroshi Inagaki's Samurai, the Legend of Musashi, in 1951, 1954, and 1955 respectively.)
Perhaps of more interest to anime fans is Kunio Katou's Tsumiki no Ie, or Le Maison en Petits Cubes, which won Best Animated Short Film. Le Maison isn't exactly done in a typical anime style, but Japanese animation it is nonetheless-- woohoo!
More trivia: the last time Japan managed to take home two awards was in 1954, when they took home both Best Costume Design and the aforementioned honorary Best Foreign Film award for Gates of Hell. (That tidbit courtesy of Tokyograph.)