In 1985, Swanson made her professional debut in the Prince video Raspberry Beret. She and Prince were friends. He wrote a song entitled "Palomino Pleasure Ride" for her. In 1987, Swanson made her feature debut in the opening scene of Lethal Weapon. She played Amanda Hunsaker, who falls to her death from a building onto the hood of a car. She performed this free-fall stunt from 35 feet into an airbag under the training of stuntman Dar Robinson. Lethal Weapon would be Swanson's first time working with Cinematographer Steven Goldblatt. She worked with Steven Goldblatt again on Charlie Wilson's War.
In 1989, Swanson joined the cast of Cheers in the recurring role of Kelly Gaines. Her character was a pretty, wealthy, naïve, Lutheran girl, who would eventually marry Woody Boyd, played by Woody Harrelson. She continued to appear in the show until the series ended in 1993.
In 1991, she had a recurring role in the series Baby Talk. In 1992, Swanson appeared on the cover of TV Guide. Swanson modeled in runway show for Ralph Lauren. In 2002, she appeared in an Automotive TV commercial in which she was seen driving a GM vehicle to pick up her husband, who emerged from a submarine that popped through thick ice.
