Josi, who played for SC Bern prior to coming over to North America, also had an assist.
Filip Forsberg and Matt Duchene also scored for Nashville. Kevin Lankinen made 15 saves.
Sven Baertschi, Romain Loeffel and Christopher DiDomenico scored for Bern. Philip Wuthrich made 27 saves.
Baertschi gave Bern a 1-0 lead with a power-play goal at 10:57 of the first period.
Josi tied it 1-1 at 17:46 when he skated down the right side and beat Wuthrich with a backhand.
Loeffel put Bern back in front 2-1 at 19:50 of the first, but Forsberg responded with a goal from in front of the net to tie it 2-2 at 6:24 of the second period.
Duchene gave the Predators a 3-2 lead at 8:03, scoring a power-play goal during a delayed penalty.
Josi pushed the lead to 4-2 at 5:54 of the third period from the left face-off dot.
DiDomenico scored with 13 seconds remaining for the 4-3 final.
Hurricanes 8, Blue Jackets 1:Martin Necas had two goals and two assists for the Carolina Hurricanes in an 8-1 win against the Columbus Blue Jackets at PNC Arena in Raleigh, North Carolina.
Derek Stepan, who is training camp on a professional tryout contract, had two goals and an assist, Brent Burns had a goal and two assists, and Jesperi Kotkaniemi, Stefan Noesen and Brady Skjei each had a goal and an assist for Carolina, which is 4-0-0 this preseason. Antti Raanta made 25 saves.
Daniil Tarasov allowed three goals on 21 shots for Columbus before being replaced by Jet Greaves, who made 19 saves.
Yegor Chinakhov's fourth goal of the preseason gave the Blue Jackets a 1-0 lead at 5:54 of the first period.
Kotkaniemi tied it 1-1 at 7:15 with a power-play goal, beating Tarasov glove side from the left face-off circle.
Noesen put the Hurricanes ahead 2-1 at 13:54 before Stepan made it 3-1 at 19:55.
Burns extended the lead to 4-1 with a power-play goal at 6:40 of the second period, and Necas made it 5-1 at 10:54.
Skjei pushed it to 6-1 at 11:51.
Stepan scored his third goal of the preseason 46 seconds into the third period to make it 7-1, and Necas also scored his third of the preseason at 17:53 for the 8-1 final.
Maple Leafs 5, Canadiens 1:William Nylander had two goals and an assist for the Toronto Maple Leafs in a 5-1 win against the Montreal Canadiens at Bell Centre in Montreal.
Alex Kerfoot scored twice, and Nicholas Robertson had three assists for Toronto. Matt Murray made 29 saves and has allowed one goal on 46 shots in two games this preseason.
Jake Allen, who signed a two-year, $7.7 million contract ($3.85 million average annual value) with Montreal on Saturday, made 26 saves.
Nylander gave the Maple Leafs a 1-0 lead with a power-play goal at 2:17 of the first period, and Zach Aston-Reese pushed it to 2-0 at 8:40.
Nylander extended the lead to 3-0 at 5:52 of the second period, corralling a pass from Robertson in front and lifting a backhand over the blocker of Allen.
Jonathan Drouin cut it to 3-1 at 14:15 of the third period. Juraj Slafkovsky, the No. 1 pick in the 2022 NHL Draft, got an assist on the play for his first point this preseason.
Kerfoot restored Toronto's three-goal lead at 15:42 before scoring his second of the game on the power play to make it 5-1 at 18:42.