Fisher stretched Nashville's lead back to two goals at 5:50.
Wilson carried the puck behind the Detroit net, emerged on the right side, and found Fisher on the left side for a shot into an open net that gave him his 10th goal of the season.
Fisher set himself up for a Gordie Howe hat trick when he fought Abdelkader late in the second period.
Miller made it 4-3 at 11:30, but Wilson's second of the game was scored 37 seconds later off a nice feed from defenseman Seth Jones, who had two assists for the second consecutive game.
"It was a good play by (Jones), and I just had to get it up over," Wilson said. "We are definitely more confident out there, and did well defensively."
Eaves netted his first goal of the season at 14:52 during a power play to again bring the Red Wings within a goal, 5-4.
Josi's empty-net, power-play goal concluded the scoring.
Henrik Zetterberg and Niklas Kronwall each had a pair of assists for Detroit.
"There were times when we were doing a lot of good things and we're sticking to the game plan, but for some reason we're losing guys up ice and we're not executing in our own zone," Kronwall said. "I thought we made it a little too easy for them at times. They got their chances a little bit too easily."
NOTES: Nashville is 15-1-2 when it has scored first this season. ... Wilson has points in three consecutive games. ... Datsyuk has 69 points in 63 career games against Nashville.