Patrick Kane had a goal and an assist, and Kevin Lankinen made 30 saves for the Blackhawks (25-39-11), who are 1-7-2 in their past 10 games.
"We were just sloppy," Kane said. "Even when we got the puck back, we gave it away too easy. They're a hard forechecking team. I think Hynes deserves a lot of credit for the way they play. You look at their roster and you think it's a beatable team, but they just play so hard, and he obviously enforces that. So he deserves a lot of credit."
Eeli Tolvanen gave the Predators a 1-0 lead at 3:22 of the first period, scoring on a one-timer from the left face-off circle. It was his first goal in 12 games.
Kane tied it 1-1 at 7:31, capping a 2-on-1 rush with a shot under Saros' legs.
Dominik Kubalik gave Chicago a 2-1 lead at 5:15 of the second period, taking Lukas Reichel's pass at the side of the crease and scoring into an open net. It was the first NHL point for Reichel, who has played 10 games.
"I'm sure it's a relief for him," Chicago coach Derek King said of Reichel, the No. 17 pick in the 2020 NHL Draft. "It was a nice play, a good heads-up play, and that's what we expect. But yeah, him getting that point is going to make him feel better. Give him a little confidence, [so he's] not squeezing the stick as much, thinking, ' got to get points. I got to get points.'"
Roman Josi tied it 2-2 at 5:58, scoring his 20th goal of the season. Josi appeared to score again 1:04 later, but the call on the ice was overturned after Chicago challenged for offside.
"Obviously, we didn't score a lot of goals the last couple games," Josi said. "We didn't like our game against Edmonton. We knew if we played our style, played the right way, we were going to get some goals and we did tonight. Big win for us."