The Devils had an opportunity to go up by two on the power play when the Predators were called for too many men on the ice with 2:46 remaining in the third, but New Jersey managed one shot on goal during the penalty.
"We had a really big penalty kill at the end, then made a really good play to get our shot," Granlund said. "I think they were playing it safe (using two defensemen on the power play), but we've done that before. That was a good job by us getting two points and a good way to start this back-to-back."
Johansen had an assist, and Saros made 25 saves in his seventh start in eight games for the Predators (11-9-2), who have won three of their past four.
Jack Hughes and Erik Haula each had two assists, and Vitek Vanecek made 20 saves for the Devils (19-4-1), who lost for the second time in their past 18 games (16-1-1).
"Even though we put an extra defenseman up there, the mindset is go for the goal on the late power play," New Jersey coach Lindy Ruff said. "I didn't like what we did. Nobody did. We wanted to attack, we wanted to try to score, but at the same time we were going to be smart and have two defensemen for both (power-play) units. The execution wasn't what we wanted."
Saros made seven saves in the third, including a pad stop against Nico Hischier on a short-handed breakaway at 13:37.
"We found a way to get it done," Nashville coach John Hynes said. "To be a top team you have to beat top teams, and we did that tonight. That was a hard-fought game. We had a big kill at the end and the guys at 6-on-5 got it done."