Kevin Lankinen allowed five goals on 22 shots and was pulled in the opening minute of the third period for the Blackhawks (21-20-5), who are 0-4-2 against the Predators this season. Malcolm Subban made eight saves.
It was the opener of a three-game series. The teams will play at Chicago on Wednesday.
"I thought we were playing well," Blackhawks coach Jeremy Colliton said. "Obviously to go down 3-1 was tough, but then we battled back and we controlled a lot of that second (period) and easily could've tied it. We want to recapture that momentum. … We certainly had our chances."
The Predators are fourth in the eight-team Discover Central Division, three points ahead of the fifth-place Dallas Stars, who also won Monday. The Blackhawks are sixth, four points behind the Predators. The top four teams will qualify for the Stanley Cup Playoffs.
"We're fighting for a playoff spot, and obviously Chicago is as well," Kunin said. "We've had that mindset for the last 20 or so games. It's a playoff mindset, and we've got to come in and do the right things every day."
Matt Duchene scored on a redirection for his first goal since Feb. 11 at 6:22 of the first period to give the Predators a 1-0 lead. It was Duchene's second game back after he missed 22 games because of a lower-body injury.
Alex DeBrincat tied it 1-1 at 15:14 with a power-play goal off a backhand pass from Pius Suter.
"We have a few breakdowns, about two minutes of poor hockey, and they score four goals," DeBrincat said. "We've got to be better, come back to play. We got some home games coming up, so we need to capitalize there."
Jarnkrok gave the Predators a 2-1 lead at 4:48 of the second period on a pass from behind the net from Mikael Granlund, who had two assists.
"[Jarnkrok's] a really good player," Granlund said. "We've been playing together quite a bit here, so it's a lot of fun to play. He's a really responsible player. He's a really smart player. There's a lot of trust out there, so we can both kind of play offense. We know there's someone who is going to be responsible, that's one thing. Offensively, we work hard and we've been getting a couple turnovers and getting some chances from those. It's been a good stretch and we've just got to keep it going."