Josi gave the Predators a 1-0 lead at 7:31 of the first period. Bernier appeared to be in position to stop Josi's shot from the face-off circle, but the puck slid underneath him.
Josi, who has scored eight points (three goals, five assists) in his past six games, is fourth in Predators history in games played behind David Legwand (956), Shea Weber (763) and Martin Erat (723).
"That 700 games is very impressive," Nashville coach John Hynes said. "Not only 700 games, but how many meaningful games he's played in and been productive, so really happy for him. It's a special night for him. He obviously had the two points, but also blocked some shots, played well."