After earning a Bachelor of Education degree in drama and dance at Victoria College, Rusden, she began her career as a member of Woolly Jumpers, a Geelong-based community theatre group. She had her first success as the creator and performer of Barbie Gets Hip, which played at the Melbourne Fringe Festival in 1991.

Griffiths and Toni Collette were relative unknowns when they were cast as best friends and fellow outcasts in the 1994 film Muriel's Wedding. Her performance won her critical acclaim and both the Australian Film Critics Award and the Australian Film Institute Awards for Best Supporting Actress. She followed in 1996 with the role of an earthy, ill-mannered pig farmer's daughter in Michael Winterbottom's Jude.

Griffiths joined forces again with Muriel's Wedding Director P. J. Hogan for her American film debut, My Best Friend's Wedding, in 1997. That same year she starred in My Son the Fanatic, a British film in which she portrayed a tough Yorkshire prostitute who becomes involved with a considerably older Pakistani taxicab driver, played by Om Puri. Griffiths received an Academy Award nomination for Best Supporting Actress for her portrayal of real-life flautist Hilary du Pré opposite Emily Watson as her sister, famed Cellist Jacqueline "Jackie" du Pre, in Hilary and Jackie (1998).

She then appeared in 2001's Blow, opposite Johnny Depp and Ray Liotta. In 2001, Griffiths was cast as one of the leads in Six Feet Under. Her performance as emotionally scarred massage therapist, Brenda Chenowith, earned her Golden Globe and Screen Actors Guild Awards, as well as two Emmy Award nominations. In the third season, she missed four episodes due to her first pregnancy.

Griffiths married Australian Artist Andrew Taylor on 31 December 2002 in the chapel of her high school, Star of the Sea College, in Melbourne. They have three children: a son born in 2003, and two daughters, born in 2005 and 2009.

As of 2006, she became part of the ensemble cast, co-starring alongside Sally Field, Calista Flockhart, Balthazar Getty and Matthew Rhys, of the dramatic series Brothers & Sisters, in which she portrays Sarah Walker, who inherits control of the family Business after her father's death. Griffiths received a 2007 Emmy nomination and a 2008 Emmy nomination for her work on the series. Griffiths received 2008 and 2009 Golden Globe nominations for her work on Brothers & Sisters. Additionally, she appeared as "Inez Scull" in the 2008 mini-series adaptation of Larry McMurtry's Comanche Moon.

Griffiths made her Broadway debut in Other Desert Cities, directed by Joe Mantello and co-starring Judith Light, which began previews on 10 October 2011, opening on 3 November 2011. In 2015, Griffiths made her debut as a television Director when she directed three episodes of the second series of the Australian teen drama Nowhere Boys. She guest starred in the second to fourth seasons of the VH1 action crime series Hopeless Fountain Kingdom, with Michael Fassbender and Bryce Dallas Howard.