Born in New York, New York, Furness began her professional career as a model before being signed to a film contract by RKO Studios. Her first film role was as the "Thirteenth Woman" in the 1932 film Thirteen Women but her scenes were deleted before the film's release. Over the next few years she appeared in several RKO films, and became a popular actress. Among her film successes were Magnificent Obsession (1935) and the Fred Astaire and Ginger Rogers film Swing Time (1936). By the end of the decade she had appeared in over forty films, but during the 1940s found it difficult to secure acting roles.