He is known for his roles in the films Syriana (2005), Art School Confidential (2006), Elvis and Anabelle (2007), The Social Network (2010), The Darkest Hour (2011), The Ides of March (2011), The Internship (2013), Horns (2013), and Spiral (2021), as well as his role as Nick Blaine in the television series The Handmaid's Tale (2017–present), which earned him a Primetime Emmy Award nomination in 2021.

[16][17] One critic who rated the film "7 out of 10" remarked that Minghella was "a talented young actor to watch, delivering a strong performance".

[18] Minghella's other November 2005 role was the political thriller Syriana, in which he played the son of George Clooney's CIA agent character.

In 2006, he starred in the Daniel Clowes adaptation Art School Confidential, a comedy directed by Terry Zwigoff.

[4] He was to play Art Bechstein in the film version of writer Michael Chabon's novel The Mysteries of Pittsburgh, but dropped out of the project due to his university schedule.

Later in 2008, Minghella played a pompous film director in How to Lose Friends & Alienate People, and was seen in a segment of the dark comedy Brief Interviews with Hideous Men.

In November 2013, it was announced that Minghella would be playing Richie Castellano in the second season of the Fox sitcom The Mindy Project.

[26] Minghella has been playing the role of Nick Blaine, an Eye in the Republic of Gilead and the love interest of June Osborne, in the Hulu dystopian series The Handmaid's Tale since 2017.

He was nominated for a Primetime Emmy Award for Outstanding Supporting Actor in a Drama Series for the role in 2021.