Artemi Panarin and Niklas Hjalmarsson scored goals for Chicago (26-12-5), which has won three in a row. Patrick Kane had his 10th multi-point game of the season with three assists. Corey Crawford made 25 saves for his 15th win.
WATCH: All Predators vs. Blackhawks highlights
"It's not really how you draw it up, but they count," said Hartman said of his final two goals, which he scored at 18:46 and 19:28. "I don't think anyone is going to remember that in a couple days."
Austin Watson made it 2-2 at 2:01 of the third for the Predators (17-16-7), but Hartman put Chicago back in front with his first goal. It withstood a video review that determined the puck hit his left hand and crossed the goal line before the net was dislodged.
"It didn't have to do with the net [coming off] for me," Nashville coach Peter Laviolette said. "It had to do with whether or not he took his hand off his stick and batted it into the net. It was difficult to tell, but certainly there was that motion that he did it. I guess you can't tell in the end whether or not he actually hit it."
Mattias Ekholm scored and Mike Fisher had two assists for Nashville, which got 26 saves from Rinne.
Chicago led 2-1 on goals by Panarin and Hjalmarsson after a first period that had 13 combined shots.
Panarin made it 1-0 at 7:45 on a one-timer from the left wing, and Hjalmarsson put the Blackhawks up 2-1 at 14:04 with a shot from the blue line for his NHL career-high fifth goal of the season.
Ekholm tied it 1-1 at 8:30 for Nashville, 45 seconds after Panarin's goal.
After going 1-4-1, the Blackhawks have defeated the Buffalo Sabres, Carolina Hurricanes and Predators to begin a four-game homestand.
"Big comeback win against Buffalo, kind of hung on there against Carolina and then you find yourself 2-2 in the third [against Nashville]," Kane said. "It's nice to get that third one and kind of build off of that."
