Detroit evened the best-of-seven, opening-round series at 1-1 and will host the next two games on Sunday and Tuesday.
The normally high-powered Detroit offense got off only 17 shots, but three of them made it past Pekka Rinne.
The Red Wings owned a 2-0 lead through one period on goals from Ian White and Cory Emmerton.
Andrei Kostitsyn tallied for Nashville 9:01 into the middle period, but Franzen restored the two-goal lead just 56 seconds later when he redirected a shot from Brad Stuart.
Nashville again drew to within one on Shea Weber's backhander with 4:44 to play, but Jimmy Howard hung on to improve his playoff record to 13-12. Howard made 24 saves.