Seth's first break came in Peter Brook's production of A Midsummer Night's Dream, which toured in 1972. Seth entered feature films in Richard Lester's Juggernaut (1974), but because subsequent filmmakers only wanted Seth for ethnic roles, his career abruptly stalled.

Seth was formerly in a relationship with Actress Lynette Davies. He was later married to author Pepita Seth, but they separated in the late 1980s and divorced in 2004.

Also in 1982, Seth played Indian author Victor Mehta in David Hare's biographical play, A Map of the World, which toured for several years in Australia, London, and New York. After the release of the multi-award-winning movie Gandhi (1982), Seth was much in demand, and when A Map of the World's Broadway run finished, his movie career took off. His work in 1984 included major roles in Indiana Jones and the Temple of Doom and David Lean's A Passage to India. Following that he played a lead in My Beautiful Laundrette (1985), and he played Pancks in Little Dorrit (1988).

Seth's film credits in the 1990s included roles in Not Without My Daughter (1991), Mississippi Masala (1991), Street Fighter (1994), and Harish Saluja's The Journey (1997). In 1993, he played the role of Haroon Amir in the television miniseries The Buddha of Suburbia, for which he was nominated a Royal Television Society award for "Best Actor – Male". In 1995, he played the role of Baba in Flight, for which he won the "Best Actor" award at the Sochi International Film Festival. In 1998, he played the leading role of Gustad Noble in the film Such a Long Journey, for which he won the Genie Award for Best Performance by an Actor in a Leading Role.

In 2001, Seth appeared in Monsoon Wedding, and he has continued working steadily in British and American films. In 2003 he played the lead in the American film Cosmopolitan, which was broadcast nationally on PBS. He also recently returned to mainstream Indian cinema with his role in the 2012 film, Ek Tha Tiger.