Justin Abdelkader and Drew Miller each had a goal for the Red Wings, who have dropped three of four. Joey MacDonald gave up three goals on 20 shots in the loss.
Nashville sits in fifth place in the Western Conference with 87 points, four back of Detroit for the fourth spot.
The Predators took a 1-0 lead on a 2-on-1 break that saw Legwand send the puck from the left to the right, where Hornqvist put it behind MacDonald 7:30 into the first.
Detroit tied the game just 13 seconds later when Miller's turnaround shot from the low-right circle snuck past Rinne.
Nashville, though, took the lead back on the power play with 8:01 to play in the first as Legwand passed the puck from the top of the right circle to the slot, where Sergei Kostitsyn one-touched it down low and his brother snuck it home.
The brothers hooked up again on the power play 4:34 into the third when Sergei passed it from the low-right side to the left and Andrei redirected it in.
Detroit made it a one-goal game with 5:25 to play on Abdelkader's wrister, but the Red Wings were unable to net the equalizer.
Detroit opened a four-game road trip and will play in Los Angeles on Tuesday...The Predators begin a four-game road swing in Phoenix on Monday...Detroit has won three of five from Nashville this season. The two will meet in Detroit on March 30 for the final regular season game between the squads.