Delany was born in New York City. After growing up in Stamford, Connecticut, she attended Phillips Academy in Andover, Massachusetts, then Wesleyan University.

She was cast as Colleen McMurphy on China Beach, airing from 1988 to 1991, bringing intense media attention to the actress. This role not only garnered two Emmy Awards, but two other Emmy nominations, and two Golden Globe nominations.

Leveraging this newfound fame, she appeared in feature films such as Light Sleeper (1992), Housesitter (1992), Tombstone (1993), and Fly Away Home (1996) and TV movies such as Promise to Keep (1991), and Wild Palms (1993).

She took on controversial roles, such as Margaret Sanger in the TV movie Choices of the Heart (1995), Mistress Lisa in the 1994 feature film Exit to Eden (adapted from the Anne Rice book), and an Emmy nominated role as a gun-owning mother in an episode of the TV series Family Law (1999) (which was not rerun, due to sponsorship withdrawal).

Delany provided voice-over work as Andrea Beaumont in the 1993 animated feature Batman: Mask of the Phantasm and Lois Lane in the Warner Bros. animated production of Superman, starting in the mid 1990s, and continuing through 2005. She was also mentioned by name in the theme song of Animaniacs, another Warner Bros. production.

During the latter part of the 1990s and early 2000s, she focused on roles in TV series, such as the short-lived Pasadena (2001) and Presidio Med (2002); TV movies like True Women (1997), Resurrection (1999), A Time to Remember (2003), and Baby for Sale (2004); and feature films by indie film producers, such as The Outfitters (1999), Mother Ghost (2002), and Spin (2003).

During this period, she found time to get back to the stage, on and off Broadway, in Translations (1995, Broadway), Dinner With Friends (2000, New York City, Los Angeles, Boston), and Much Ado About Nothing (2003, San Diego).

From 2004 to 2006, Delany played many guest roles on TV shows such as Law & Order: Special Victims Unit, Boston Legal, Kojak, Related, The L Word, and Battlestar Galactica. Dana also starred in the short-lived TV series Kidnapped (2006).

In 2007, Delany took parts in the films A Beautiful Life, Camp Hope, and Multiple Sarcasms, and then joined the cast of the TV series Desperate Housewives for the 2007/2008 season.

Since the mid-1990s, Delany has served on the board of the Scleroderma Research Foundation, and with her friend Sharon Monsky, she helped campaign for support in finding a cure for scleroderma. Working with director Bob Saget, Dana starred in the TV movie For Hope (1996), based on Saget's sister Gay, who had died as a result of the disease.

Since the mid-1990s, she has had a notable World Wide Web presence. She has participated in several online chat events promoting various projects. Her Official Web Site, online since 1996, includes a guestbook in which she participates.