Granlund had a goal and an assist, and Juuse Saros made 25 saves for the Predators (25-21-2).
"You know they're a good rush team, they get time and space, they're going to be able to make plays," Nashville coach John Hynes said. "We weren't stiff enough in that area with the structure or commitment that we need to play with in that area."
The teams play the last of the three-game set here Friday. The Predators won 5-2 in Nashville on Monday.
Nashville is in fourth place in the eight-team Discover Central Division, two points ahead of the Dallas Stars, who have three games in hand. Chicago is sixth, three points behind Nashville. The top four teams will qualify for the Stanley Cup Playoffs.
"We did get one point out of the game, we did a lot of good things in the game," Hynes said. "We certainly played a good game. We had a stretch in the third period where it looks like we let our foot off the gas a little bit, and that's something you can't do against any team.
"You have to take the point out of it, you have to take the lessons out of why we gave up the lead the way that we did, and there's a lot of good things in the game you come back to."