Gillespie started out as an intern at ad agency J. Walter Thompson, New York. He then moved on to D’Arcy Masius Benton & Bowles, BBDO, Deutsch, and Ammirati & Puris, first as an art director, later as a creative director. After eight years working on the agency side he moved into directing in 1995. Based on the strength of his spec reel and agency experience, he gained representation by production company Fahrenheit Films in late 1995. One year later, he signed with Coppos Films. He has been with MJZ since 2000 and continues to work as a commercial director, commonly working with cinematographers Adam Kimmel and Rodrigo Prieto. Following nominations in 2001 and 2002 in the Directors Guild of America Award category for “Outstanding Directorial Achievement in Commercials”, he won in 2006 for his Ameriquest and Altoids commercials. He also won a Golden Lion Award at 2005’s Cannes Lions International Advertising Festival, and two of his commercials belong to the Museum of Modern Art in Midtown Manhattan’s permanent collection.

Gillespie directed several episodes, including the pilot, of the first season of Steven Spielberg and Diablo Cody’s television series The United States of Tara. He was set to re-team with Lars and the Real Girl lead actor Ryan Gosling for Dallas Buyers Club, a film telling the true story of Ron Woodroof, an electrician given six months to live after he was diagnosed with AIDS, but used a variety of drugs which he smuggled to other AIDS patients to live for another six years. However, the directing job instead went to Jean-Marc Vallée and Matthew McConaughey as Ron Woodroof. In March 2010, it was announced that Gillespie would direct the Fright Night remake, starring Colin Farrell, Anton Yelchin and Toni Collette for the lead roles. Gillespie and Sam Worthington won the 2009 Australians in Film Breakthrough Award.

In 2011, he directed the music video for Kid Cudi’s single, “No One Believes Me”. Gillsespie finalized his contract to direct an adaptation of Pride and Prejudice and Zombies on 18 April 2011. but he later left the film. In April 2014, it was announced that Gillespie would direct the film The Finest Hours about the Coast Guard who tries to save the crews of two oil tankers in 1952. Chris Pine, Casey Affleck, Josh Stewart, Graham McTavish and Kyle Gallner star in the film for Walt Disney Pictures. The sets for the film were made in Quincy, Massachusetts.

Gillespie directed I, Tonya (2017), a biographical film revolving around figure skater Tonya Harding, starring Margot Robbie, Sebastian Stan and Allison Janney. Gillespie has been announced to direct the Gregg Allman’s autobiography novel, My Cross to Bear into a feature film. In December 2018, it was announced that Gillespie will be replacing Alex Timbers (due to the latter’s scheduling conflicts) as director for Disney’s live-action spin-off of One Hundred and One Dalmatians; titled as Cruella, with Emma Stone set to portray Cruella de Vil.