Nicklas Lidstrom, Jiri Hudler and Tomas Holmstrom also scored for Detroit, which won its fifth straight.
Datsyuk has 14 points - two goals and 12 assists - in his last five games, Zetterberg has three goals and nine assists while scoring at least a point in six straight games, and Holmstrom has nine goals in his last 10 games.
Greg Zanon got his first NHL goal, and Jordin Tootoo and Dan Hamhuis also scored for Nashville, which snapped its six-game winning streak.