Moses began his career appearing in the ABC daytime soap operaOne Life to Live in 1983. Also in 1983, he appeared in the Broadway production of The Slab Boys Trilogy starring Kevin Bacon and Sean Penn. He later played Ulysses S. Grant in the ABC miniseries North and South and guest-starred on Family Ties, The Golden Girls and Matlock. Moses also appeared in a number of films by director Oliver Stone, such as Platoon, Born on the Fourth of July and The Doors. Moses played supporting roles in a number of movies, including Gettysburg, Deep Impact, One Man's Hero, Big Momma's House 2, Swing Vote, Cesar Chavez and Bombshell. His only leading film role was in the 1997 romantic comedy-drama Just in Time directed by Shawn Levy. Moses also appeared in several made-for-television movies and was regular cast member in the short-lived sitcoms Grand and The Single Guy. He played Woodbury Kane in the 1997 miniseries Rough Riders and also guest-starred on Touched by an Angel , ', ER, The West Wing, NYPD Blue, Drop Dead Diva, ', , Scandal and Grey's Anatomy. In 2004, Moses was cast as Paul Young in the ABC mystery comedy-drama series Desperate Housewives. As the disturbed husband of the deceased Mary Alice Young, Paul was a key character in the show's original main mystery. He left the series as regular cast member after two seasons, but still made some guest appearances in the third season. Moses returned to the series as a series regular after appearing briefly in the sixth-season finale, and was regular through the 2010–11 season. Along with the rest of the cast, he received two Screen Actors Guild Award for Outstanding Performance by an Ensemble in a Comedy Series in 2005 and 2006. In 2007, Moses joined the cast of AMC period drama series Mad Men playing a recurring role as Herman "Duck" Phillips. In 2009, he received another Screen Actors Guild Award, this time for Outstanding Performance by an Ensemble in a Drama Series. The series ended in 2014. In 2012, he had a recurring role in the second season of AMC crime drama The Killing. In 2014, he co-starred in the fourth season of the Showtime political dramaHomeland playing Dennis Boyd. Moses also had a recurring roles on Manhattan, Man Seeking Woman, Law & Order True Crime and Salvation. He played the recurring roles of President in the TNT series The Last Ship from 2015 to 2018, and in the Telemundo/Netflix La Reina del Sur. In 2020, he was regular cast member in the Fox crime drama Deputy, which, however, was cancelled after one season.