Jesper Fast, Andrei Svechnikov and Teuvo Teravainen scored, and Brett Pesce had two assists for the Hurricanes, who have won their first two games of the season.
"I just tried to continue my process of focusing on the next shot," Andersen said. "You can't really focus on too much else. They have a bigger team. You just want to stay in the fight and do the next shift. That's what the players do. As goalies, it's the next shot. Like I said before, I think we stayed in the fight and got another two points."
Ryan Johansen had a goal and an assist, and Juuse Saros made 29 saves for the Predators, who have lost their first two games.
"I thought we played pretty well," Nashville coach John Hynes said. "I thought in the first period we were under duress a little bit, and really it was self-inflicted by us. Just our execution coming out, I thought we were rimming pucks too much along the wall and we didn't play with enough poise in our own zone.
"But I thought we did a good job in the second and third. I think when you look at the style of game that we want to play and being able to put them under duress and give ourselves a chance, I think there's lots to build on."
Svechnikov gave the Hurricanes a 2-1 lead at 14:00 of the third period on a wrist shot from the left face-off circle on the rush. He took a pass from Martin Necas and beat Saros short side.
"[Goaltending] was the difference, obviously," Carolina coach Rod Brind'Amour said. "I haven't seen a lot of games like that in the three years that I've been doing this, where clearly the goaltender was the reason we won the game or we needed him too. It's usually the goalies are playing good, but we're playing well. We didn't play a very good game in front of him, but he came up huge."