Philip Tomasino and Colton Sissons also scored, Yakov Trenin had two assists, and Juuse Saros made 27 saves for the Predators (31-23-6), who have won five of their past six, including the first two of a season-long six-game road trip.
Nashville is five points behind the Colorado Avalanche for the second wild card into the Stanley Cup Playoffs from the Western Conference.
"It's been a hectic week, obviously, with all the trades and guys in and out," Predators coach John Hynes said. "Now to be able to go on the road with a lot of new guys, and it's a nice road trip, too, where we have a lot of games, but there are some days off where guys can spend more time together, which I think can be good, and getting out of Nashville for a little bit and being together on the road and keep pushing forward."
Seth Jones scored, and Mrazek made 22 saves for the Blackhawks (21-36-5), who have been outscored 16-6 during a four-game losing streak.
"I thought the first part of the first two periods we played better, and then we kind of dropped off," Chicago coach Luke Richardson said. "We were more physical, skating, had the puck, driving offensive plays more … and then we seemed to be a little bit too much in the [defensive] zone and not enough in the [offensive] zone.
"But our guys played and our guys played to the game plan well. It kind of fell off a little bit for pace for me, but I think we're still trying to find ourselves."
Jones gave the Blackhawks a 1-0 lead 37 seconds into the first period when he tipped in a pass by Andreas Athanasiou to finish a give-and-go.
"I think it's always nice to start great," Chicago forward MacKenzie Entwistle said. "First shift we get a goal, then I thought we battled pretty hard most of the game. We limited their chances, and Mrazek played great. Obviously, it's frustrating not being able to pull away with the win, but I thought we generated some offense. We had some chances, just maybe a little bit of puck luck and the game may be a little different."