The Predators cut their deficit in the Western Conference semifinals to 2-1 and will try to even the series Friday at home.
Rinne earned the shutout in his 26th post-season appearance and handed Phoenix its first road loss of the playoffs. The Coyotes won all three road games against Chicago in the opening round.
Rinne led the NHL in regular-season wins this year with 43 and bounced back from a struggling performance in Game 2 of the series in which he allowed five goals on 39 shots.
Notable deaths of 2014 [PHOTOS]