Taking the name George Jenesky, Dunn performed over seven seasons (1981–90) in the NBC daytime soap opera, Days of Our Lives. His character, Nick Corelli, became a fan favorite, a despicable pimp who evolved into a romantic lead and one of the show's main characters. Nick's murder was one of the series' notable whodunits.

He has made numerous appearances in films and on television, frequently as the villain. In the mid-1990s he returned to the name Conrad Dunn and began working extensively in Canada as well as the U.S. Notable TV roles include an antagonistic juror in the USA Network film, We the Jury (1996), a remorseless mobster in two CBS miniseries (1997–98) adapted from Mario Puzo's The Last Don, and the arch villain in the 2000 pilot for TNT's supernatural drama series Witchblade. In 2001 he joined the principal cast of the A&E TV series, Nero Wolfe (2001–02), portraying the superlatively competent freelance detective Saul Panzer for two seasons. His later film appearances include Chicago (2001), Owning Mahowny (2003) and Ving Rhames' Animal 2 (2007).

Dunn had his own theatre company, and his stage credits include a 1994 production of Edward Albee's The Zoo Story simultaneously performed in American Sign Language. "Notwithstanding the value of bringing this important work to a non-hearing audience, the Energy of the gestures generated by the actors actually underscores the emotional impact of their fateful encounter," wrote Variety.