Shun made his TV debut in NHK's drama Hachidai Shogun Yoshimune in 1995. In 1998, by playing the bullied and abused child Noboru Yoshikawa in the dramaGreat Teacher Onizuka, Shun started to be recognized by the public. His act in that drama attracted the attention, and brought him bigger roles. In 2000, he played a deaf person in Summer Snow. Two years later, he starred in the popular drama Gokusen, in which he played a part of a bully, rather than the bullied as he did in Great Teacher Onizuka. In 2005, Shun lent his voice as a voice actor in Fullmetal Alchemist the Movie: Conqueror of Shamballa together with his brother Ryo Oguri.
Shun rose to prominence after his breakthrough role as 'Hanazawa Rui' in the popular drama Hana Yori Dango in 2005, and his first lead role as 'Shinichi Kudo' in the first Detective Conan live movie Detective Conan: Shinichi Kudo's Written Challenge in 2006. In 2007, he starred in the drama Hanazakari no Kimitachi e as 'Izumi Sano', cooperating with Toma Ikuta and Maki Horikita. In 2008, Oguri took up another lead drama role in Binbō Danshi by playing a poor college student named 'Kazumi Koyama'. At the same year, he played in the drama Tokyo Dogs as an American detective 'So Takakura' in the leading place. In 2009, Oguri lent his voice as a voice actor once again in Wangan Midnight as 'Akio Asakura'.
He reunited with Hana Yori Dango co-star Mao Inoue for the drama Jūi Dolittle (獣医ドリトル,Veterinarian Dolittle), which began airing in October 2010.In 2012, he costarred with Satomi Ishihara in Fuji TV's Rich man, poor woman as a young wealthy man 'Toru Hyuga', which earned him the first Best Actor award in 74th Drama Academy Award. He also starred in anime adapted drama Nobunaga Concerto, which was aired in 2014 as both 'Saburo' and 'Nobunaga Oda' and in live movie Lupin the third as Lupin III.
In 2015, he reunited with Toma Ikuta after seven years in the TBS drama Ouroboros as 'Tatsuya Danno'.
Oguri is also a director. His first directorial debut was directing a commercial in 2009, but his first major directorial debut on the big screen was a movie titled Surely Someday, which was released in July 17, 2010 nationwide in Japan. Oguri cast several of his good friends within the entertainment industry in the movie, such as Keisuke Koide as the lead starring role, Actresses Mao Inoue and Aya Ueto as cameos and himself also made a cameo appearance in the movie.