The Ruidoso, New Mexico native was auspiciously discovered by screenwriter Mark Medoff at a youth acting camp. Medoff recommended Harris for the film "Clara's Heart" (1988), and the actor made his feature debut starring as a sensitive young boy dealing with his parents' divorce who cultivates a meaningful friendship with his Jamaican housekeeper (Whoopi Goldberg). He quickly racked up television credits, including appearances in the TV-movies "Too Good to Be True" (NBC, 1988) "Home Fires Burning" (CBS, 1989), "Cold Sassy Tree" (TNT, 1989) and a starring guest role in "Blues for Buder" (ABC, 1989), one of the series of "B.L. Stryker" detective TV movies, starring Burt Reynolds. That same year he landed the role of the pubescent "Doogie Howser, M.D.", likably playing the sixteen-year-old medical school graduate, dealing with his patients and parents as he struggled through his residency and adolescence simultaneously. To many viewers, Harris became inextricable from the role, and his skillful, award-winning performance as the young idealistic medical professional threatened to limit his future career prospects upon the series' 1992 demise.

While on "Doogie Howser, M.D." and immediately following, Harris kept busy with a spate of television appearances in longforms and series guest roles. 1991 alone saw him take parts on "Blossom" (NBC), "Carol & Company" (CBS) and "The Simpsons" (Fox). The voice work of the latter prepared him for a regular starring role on the short-lived politically themed ABC prime-time animated series "Capitol Critters" (1992), playing Max, a country mouse who ends up in Washington, DC. Featured guest parts on "Quantum Leap" (NBC) and "Murder, She Wrote" (CBS) also came in 1992, before he took on a series of characters in fact-based TV movies, most notably in the true crime NBC production "A Family Torn Apart" and CBS' "Snowbound: The Jim and Jennifer Stolpa Story", playing a man who, along with his wife and five-month-old child, survives after days trapped in a Nevada avalanche. He could additionally be seen in the 1995 telepics "Not Our Son" (CBS), "My Antonia" (USA Network), "The Man in the Attic" (Showtime) and "Legacy of Sin: The William Coit Story" (Fox). After time away from television to pursue stage roles and feature work, Harris returned with a starring turn as a young successful businessman on a journey to self-discovery in the 1998 CBS holiday offering "The Christmas Wish" and took a supporting role the following year as King Charles VII opposite Leelee Sobieski's "Joan of Arc" (also CBS). He returned to regular series work in NBC's "Stark Raving Mad" in 1999, starring as the neurotic, germ-phobic editor of a zany horror novelist (Tony Shalhoub). The series' plum time slot (nestled between heavy hitters "Frasier" and "ER") and highly capable, watchable performances by Harris and Shalhoub helped to propel this otherwise by-the-numbers sitcom.

After a nine year absence from features, Harris returned to the big screen with a supporting role in Paul Verhoeven's sci-fi actioner "Starship Troopers" (1997) and could be seen that same year alongside Matthew Lillard in the independent drama "The Animal Room". 1998 saw him take on the role of a Harvard Law student who gets emotionally involved after being hired to sire the child of a successful, infertile couple (Madeline Stowe and William Hurt) in the 1930s-set drama "The Proposition" (1998). He would follow up these little-seen roles with a turn in "The Next Best Thing" (lensed 1999), starring Madonna and Rupert Everett respectively as a woman and her gay male friend who decide to have a child together, with dramatic repercussions.

While the small screen afforded Harris fame and a comfortable lifestyle, the actor had been interested in pursuing stage work from the beginnings of his career. He made his debut at the La Jolla Playhouse in 1993, portraying a young man who runs across unimaginable hardships in pursuit of the American dream in "Luck, Pluck and Virtue", James Lapine's satirical take on the Horatio Alger success story. This role showcased Harris' potential as a charismatic stage player with a talent for physical comedy. In 1997 he was cast in "Rent", originating the role of Mark, the bleached blonde aspiring filmmaker and the piece's narrator, on the Los Angeles stage. Harris received positive reviews for his performance, his strong singing voice and deft moves proving him a surprisingly gifted musical theater player. He followed up playing Romeo to Emily Bergl's Juliet in a 1998 Old Globe Theater production of the Shakespeare classic, before being touted by critics as a highlight of a 1999 Los Angeles concert version of the Sondheim musical "Sweeney Todd", appearing in the star-studded cast alongside Kelsey Grammer and Christine Baranski.