Matt Duchene had a goal and an assist, Johansen scored, and Juuse Saros made 27 saves for the Predators (41-25-4), who have won four of five and moved four points back of the St. Louis Blues for third in the Central Division.
Nashville is also two points ahead of the Dallas Stars for the first wild card from the Western Conference.
"I think it's a complete team effort this year," Josi said. "Obviously, some guys are having great years, which is awesome, but it's not just the stats, it's everyone doing their job, which makes it so much fun to play on this team."
Mathieu Joseph and Josh Norris scored, and Anton Forsberg made 31 saves for the Senators (26-38-6), who had won three straight.
"We had breakaways, great looks, and Saros was the difference," Ottawa coach D.J. Smith said. "We got in there and I thought we overthought it. We got in our own minds. I thought we had a lot of good games by a lot of guys."
Duchene gave the Predators a 1-0 lead at 8:32 of the first period when he one-timed a cross-ice pass from Mikael Granlund on a 2-on-1.
Joseph tied it 1-1 at 15:32 of the second period, taking a stretch pass from Erik Brannstrom and scoring blocker side on a breakaway.
"I think with my speed I can disrupt a lot of things, and [my teammates'] skills just take over," Joseph said. "I'm just trying to move my feet as much as possible and they're finding me, and I'm also finding them."
Norris made it 2-1 at 4:36 of the third period when he knocked in the rebound after his initial shot went off Nashville defenseman Dante Fabbro.
Tanner Jeannot tied it 2-2 at 7:48, tipping Josi's one-timer from the point.
"No matter how much success he's had, he's the same guy," Nashville coach John Hynes said of Josi. "He's humble, he works hard, he's a great teammate, he's a coachable player. I think that's what makes him special. And that's what makes him captain of the team."
