Rinne collected his 41st victory of the season, tying him with Pittsburgh's Marc-Andre Fleury for the league lead, as the Predators vaulted over idle Detroit for sole possession of the West's fourth playoff seed.
The sixth-seeded Blackhawks, meanwhile, saw their five-game winning streak snapped, managing only a single goal from Viktor Stalberg.
Corey Crawford was pulled after yielding four goals on just 15 shots.
Ray Emery entered and turned aside 7-of-9 shots the rest of the way for Chicago.
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend
Charlize Theron not engaged to Sean Penn 'yet'