Rinne was especially active in the third period, when he made 18 saves as the Red Wings scrambled to get back into the contest.
The Finnish netminder helped the Predators win their first-ever playoff contest in Detroit and take the advantage in their Western Conference quarterfinal series.
Kevin Klein notched a goal and an assist and made a stick save to prevent a Detroit goal in the final period.
Sergei Kostitsyn scored with 3 1/2 minutes left for a much-needed insurance tally and Shea Weber also found the net for Nashville.
Jimmy Howard 19 saves in Detroit's loss.