Arvidsson, who missed a 3-2 shootout win against Detroit on Tuesday with an upper-body injury, finished his third NHL hat trick with his first NHL penalty-shot goal.
"That's pretty good for a birthday," Arvidsson said.
Juuse Saros made 25 saves for the Predators (22-18-1), who have won nine of their past 10 games.
"We're a pretty confident group, and we are on a mission," Nashville forward Erik Haula said. "We know we have a good team, but we've got 15 games to go and we have to keep the pedal down."
Nashville finished the season series against Detroit 6-2-0, including another 7-1 win at home on March 25.
"We've had a few games lately where we haven't responded well to falling behind, and that results in games like this," Red Wings coach Jeff Blashill said. "This was a major step backward."
Jonathan Bernier made 25 saves for the Red Wings (13-23-6) in his first game since sustaining a lower-body injury March 18.
"We hung [Bernier] out to dry tonight, and that's on every one of us," Detroit forward Luke Glendening said. "Here's a guy who has been great for us all season and is coming back from an injury, and we didn't do anything to help him."