Andrei Kostitsyn supplied the lone goal in the 4.
Martin Erat registered a goal and two assists for the Predators, who squandered leads of 1-0, 2-1 and 4-2. Pekka Rinne made 31 saves to earn his league-leading 39th win of the season.
Nashville has won three games in a row and sits fifth in the Western Conference standings with 89 points, two behind Detroit.
Mike Smith also stopped 31 shots.
The point earned gives Phoenix 79 on the season, one more than eighth-place Colorado and two back of the Pacific Division-leading Dallas Stars.