He played Bob Morales, the real-life ex-convict and biker half-brother of 1950s rock and roll singer Ritchie Valens, in La Bamba (1987).

His first professional performances were in theater and television in New York. His first film was Bad Boys (1983), about rival teenagers sentenced to a Juvenile correction facility. Morales appeared in a 1985 episode of the TV series Fame. He co-starred with Burt Lancaster in the 1986 NBC miniseries On Wings of Eagles, playing the Iranian Rashid, the hero of a true story about Ross Perot. Morales also appeared in Miami Vice, The Equalizer, and 24.

In the 1990s, he guest-starred on episodes of The Outer Limits, Tales from the Crypt, and two shorter-lived series, L.A. Doctors and The Hunger. He appeared in a two-part episode of Family Law in 2000. He was part of the main cast of the long-running series NYPD Blue for three and a half seasons, from 2001 to 2004, as the head of the 15th precinct detective squad.

Morales's first name is frequently used in crossword puzzles because its rare construction (it is a four-letter word in English that is seventy-five percent vowels, including the first and last letters) makes it a prize for crossword constructors. One crossword clue website estimated that between 1994 and 2016, "ESAI" had been used as a crossword answer over 100 times in American papers such as The New York Times, The Los Angeles Times, and The Washington Post.

He played a drug dealer named Lulu in the 2002 film Paid in Full. In 2005, he was a voice actor in the video game True Crime: New York City, playing Sgt. Victor Navarro.

In 2005, Morales (along with Mercedes Ruehl) received the Rita Moreno HOLA Award for Excellence from the Hispanic Organization of Latin Actors (HOLA).

Morales was cast in the film American Fusion (2005), and on June 19, 2006, he joined the cast of the Fox series Vanished, as FBI agent Michael Tyner; the series ran for one season. In 2007, Morales appeared in an episode of the USA Network drama series Burn Notice, as a Cuban shopkeeper being shaken down for "protection" money by local Criminals. In early 2008, Morales had a role in the CBS drama Jericho, as Major Edward Beck. He appeared in all seven episodes of the shortened second season That same year, he appeared in Kill Kill Faster Faster, a film noir based on the novel of the same name by Joel Rose.

In a February 28, 2007, all-star benefit reading of The Gift of Peace at UCLA's Freud Playhouse, he portrayed a hopeful member of a struggling immigrant family, performing alongside actors Ed Asner, Barbara Bain, Amy Brenneman, George Coe, Wendie Malick, and James Pickens, Jr.. The play was an open appeal and fundraiser for passage of U.S. House Resolution 808, which sought to establish a Cabinet-level "Department of Peace" in the U.S. government, to be funded by a two percent diversion of the Pentagon's annual budget.

In May 2008, it was announced that Morales would play the role of Joseph Adama in the science fiction television series Caprica – Syfy's prequel to the series Battlestar Galactica. The series, though highly anticipated, only ran for one season in 2010. In 2009, he served as an official festival judge for the Noor Iranian Film Festival in Los Angeles.

Morales is a vegetarian. He and girlfriend Elvimar Silva had a daughter, Mariana Oliveira, on September 24, 2010.

In 2011, Morales starred in the drama film Gun Hill Road as Enrique, and in the web drama Los Americans airing on PIC.tv. In March 2015 Robert Rodriguez cast him as Lord Amancio Malvado for the horror drama series From Dusk till Dawn: The Series., and also Morales worked with Yvonne DeLaRosa, Lupe Ontiveros and JC Gonzalez in Los Americans, an Internet program that was launched in May 2011.

In 2017, Morales was cast in the Netflix series Ozark.