Kozak made her feature debut in the women-in-jeopardy thriller "The House on Sorority Row" (1983) earning favorable notices for her performance. She spent almost four years in NYC on daytime serials ("Texas" and "Guiding Light") before moving to California to join the cast of the NBC soap "Santa Barbara". Playing a virginal nun who falls in love with the scion of the wealthy Capwell family, Kozak earned a spot in the history books for her character's unusual death: crushed by a neon letter "C" that fell from a hotel marquee.
Segueing into features, Kozak played small but indelible roles in "When Harry Met Sally" and "Parenthood" (both 1989) before graduating to leading roles in such diverse features as "Necessary Roughness", "The Taking of Beverly Hills" and "All I Want for Christmas" (all 1991).
Kozak alternated between film and TV, appearing regularly in three series: "Knightwatch" (ABC, 1988) as a member of a volunteer community-watch group; "Harts of the West" (CBS, 1993) as Beau Bridges' wife; and the sitcom "Bringing Up Jack" (ABC, 1995). Among her numerous other TV appearances were memorable turns as a wife accused of murdering her elderly husband on "L.A. Law" (NBC, 1991) and as NEW YORK POST reporter Amy Pagnozzi in "Beyond Control: The Amy Fisher Story" (ABC, 1993). Kozak also sparkled in the little seen comedy feature "The Favor" (1994) and subsequently appeared opposite Mark Harmon in the children's adventure "Magic in the Water" and in the first episode of Harmon's short-lived ABC detective series "Charlie Grace" as his ex-wife (both 1995).