At 13:59 of the first period, Nashville opened the scoring after Wings forward Adam Erne went to the box for interference.
The Predators quickly took advantage of the power play as Roman Josi took a pass from Eeli Tolvanen at the point and fired a slap shot into a sea of bodies in front of Greiss. With all the traffic in front, Greiss never saw the puck and Nashville center Mikael Granlund tipped the shot into the net to give the Predators a 1-0 lead.
The Predators made it a 2-0 game 10:41 into the second period when Yakov Trenin carried the puck into the zone and behind the Red Wings net, bumping into Greiss and forcing him to lose his stick. Trenin's wraparound shot was stopped by Greiss but Mathieu Olivier was right on the doorstep and easily poked the rebound into the net.
It looked like the Predators made it a 3-0 game two minutes later when Granlund deposited another rebound into the back of the net, but Red Wings coach Jeff Blashill challenged for goalie interference on Calle Jarnkrok and the goal was overturned.
But the Wings couldn't take advantage of the overturned call and the Predators took the 2-0 lead into the second intermission.
Detroit had some hope with a six-on-four opportunity with less than two minutes to go in regulation after pulling Greiss and a delay of game penalty to Nashville, but the Wings' frustration continued as they were unable to solve Predators goalie Juuse Saros, resulting in a scoreless third period.
Saros made 31 saves on the night for his first shutout of the season.
The Red Wings will look to right the ship Thursday night in the series finale against the Predators. Puck drop from Bridgestone Arena is set for 8 p.m. ET, with the action broadcast on FOX Sports Detroit and 97.1 The Ticket.