It was his second shutout this season and 13th in the NHL. He is 6-2-0 with a 1.13 goals-against average and .968 save percentage in his past eight starts.
"I think we've found our identity lately and we've had these big character wins lately," Saros said. "We're moving in the right direction, but there's also a lot of games left so we've just got to keep our foot on the gas."
Eeli Tolvanen, Colton Sissons and Luke Kunin scored for the Predators (20-18-1), who have won seven of their past eight games. Nashville is 5-0-0 against Chicago this season.
"We understand how important these games are, especially with these games that are head-to-head with these teams that are right neck and neck with us," Sissons said. "We've been able to rise to the occasion and not succumb to that pressure and make mistakes all night long. We're pretty comfortable right now, and we've built some confidence over the last few weeks here."
Kevin Lankinen made 18 saves for the Blackhawks (17-17-5), who have lost two straight and four of their past five.
"Obviously it's tough," Chicago defenseman Duncan Keith said. "It was a huge game, and these are the biggest games right now of the year. It's a tough loss but we did a lot of good things 5-on-5. Unfortunately, special teams, they scored a quick power-play goal in the first and then we had a tough power play and they ended up getting a penalty shot. Every goal is huge, especially this time of year, and it'd be nice to try to get that first one and carry some momentum."