In 1984, he produced the Talking Heads concert film Stop Making Sense with Director Jonathan Demme. That initiated a successful run as a music supervisor, on such films as Something Wild, Colors, Modern Girls and Married to the Mob, among many others. In 1991, Producer Goetzman and Director Demme again collaborated to make The Silence of the Lambs, which garnered the top five Academy Awards including Best Picture.

In 1993, Goetzman was executive Producer of Demme's Philadelphia, starring Tom Hanks, beginning a working relationship with Hanks. Goetzman co-produced Hanks's 1996 directorial debut, That Thing You Do!. The two then co-founded The Playtone Company in 1998. Since then, Goetzman has produced hit films including My Big Fat Greek Wedding, The Polar Express, Charlie Wilson's War and Mamma Mia!. Goetzman has also received several Emmy Awards for HBO mini-series Band of Brothers, The Pacific, John Adams, Game Change and Olive Kitteridge.

Goetzman is executive Producer (with Tom Hanks and Mark Herzog) of the CNN exclusive documentary miniseries The Sixties (2014), The Seventies (2015) and The Eighties (2016).