The goal was Smith's first of the year. He had 14 goals as a rookie last season.
Wilson's assist extended his career-high point streak to five games.
Bourque doubled the Nashville lead at 10:41 of the first when he deflected Scott Hannan's slap shot from the left point by Howard on the short side.
Howard left the game less than a minute after Bourque's goal with an upper-body injury. He did not return.
Howard stopped five of the seven shots he faced in 11:22 of ice time before he was replaced by Gustavsson.
Cleary scored a short-handed goal with 4:59 left in the first and Detroit tied it at 11:33 of the third on a goal by Tootoo, a former Predator.
"I thought we battled hard, and I thought we had lots of good players," Detroit coach Mike Babcock said. In the end, we didn't have enough and didn't get it done. In this league, we don't get many moral victories."
Nashville regained the lead at 12:54 on Josi's first goal of the season, but Datsyuk tied it again at 3 just 36 seconds later.
"They had a big push in the third period," said Nashville goalie Pekka Rinne, who made 26 saves. "We have to manage the game better even though they were pushing hard."
NOTES: Tootoo played his first road game in Nashville. He spent the first eight years of his NHL career with the Predators. ... Weber has points in four consecutive games. ... Hannan's assist on Bourque's goal was his first point as a Predator.