Simultaneous to moving from Opovo to Belgrade to continue his studies, 14-year-old Bjelogrlić also debuted in movies playing a memorable role of Sava Jovanović Sirogojno in Boško Buha, a 1978 film that achieved sizable popularity. He followed that up in the coming years with other roles in TV series, short, and feature films.

By mid-1980s, Bjelogrlić was an established young actor in SFR Yugoslavia. In 1985 he appeared in Bal na vodi as part of an ensamble cast of his peers such as Srđan Todorović, Nebojša Bakočević, Goran Radaković, and Gala Videnović. In 1987, he became one of the central cast members on the hugely popular drama television series Bolji život. Playing the role of Boba Popadić made Bjelogrlić a bona fide recognizable star all across the country.

He is considered somewhat of a "Serbian Robert Redford", by many. His monotone voice and tired face leads him to be cast as a gangster or criminal figure in movies such as Rane (The Wounds), where he plays a hot-headed Serbian mafioso, with a short temper that only Dragan Bjelogrlić could provide for the movie that's considered one of the cult Serbian gangster movies, especially it being with a focus on the Yugoslav Wars . His brother Goran Bjelogrlić is a film producer. His 2010 film Montevideo, God Bless You! was selected as the Serbian entry for the Best Foreign Language Film at the 84th Academy Awards, but it did not make the final shortlist. The sequel, See You in Montevideo, was released in 2014.