The Canucks were 0-for-5 on the power play and are 0-for-17 the past four games.
"They weren't very good. It's pretty simple," coach Travis Green said of the power play.
Neither was the penalty kill.
Josi scored on a point shot on the power play past a screened Demko to put the Predators ahead 1-0 at 5:49 of the first period.
Boeser tied it 1-1 at 19:51 after a cross-ice pass put him alone at the bottom of the left face-off circle. Saros slid out at Boeser, who deked around him and tucked the puck into the empty net.
"I just knew I had time once I got the puck, and instincts just kind of took over from there," Boeser said.
Hoglander put the Canucks ahead 2-1 with a similar goal at 10:08 of the second period, faking a shot alone in the slot then stickhandling around Saros for his first goal of the season.
Duchene tied it 2-2 on a breakaway at 12:26, getting behind the defense on a pass from Granlund and scoring with a backhand deke.
Duchene has five points (three goals, two assists) during a three-game point streak, and 10 points (five goals, five assists) in 11 games after scoring 13 points (six goals, seven assists) in 34 games last season.
"I just think he's come back with the right mindset this year," Hines said. "It all came back to him playing fast, skating, being competitive. That allows his skill to come out. He's assertive, he's attacking at the right times."
Tomasino put Nashville ahead 3-2 on a power play at 19:15. Luke Kunin made a cross-crease pass from the goal line on Demko's right to Tomasino alone inside the far face-off dot, and he lifted a quick shot over the sprawling goalie.