After falling behind by three goals in the second period and trailing by one late in regulation, the Blackhawks tied it with 1:13 left in the third period and won 5-4 in a shootout to remain atop the Central Division.
Providing the opportunity to win was forward Bryan Bickell, whose goal off a rebound tied it 4-4 with the Chicago net empty.
The forwards on the ice were scheduled to come off for a line change; they stayed out a little longer and it paid off.
"We went up and down about three or four times," Bickell said. "We probably had about a minute on the shift and we should've changed, but [Brandon Saad] had good speed and we just saw the net. We got bold and didn't recognize how much time was on the clock. It's nice to see it go in and help out the team."
Chicago (25-10-2) next plays the Washington Capitals at Nationals Park in Washington, D.C., on New Year's Day in the 2015 Bridgestone NHL Winter Classic (1 p.m. ET; NBC, CBC, TVA Sports).
Crawford and Nashville's Pekka Rinne (38 saves) each made great saves in overtime to keep the game tied after facing a combined 82 shots in regulation.
Toews beat Rinne with a shot between the pads in the shootout, which ended after a wrist shot by Predators forward Filip Forsberg went wide of the net in the top of third. Crawford made saves against defenseman Ryan Ellis and forward Craig Smith.
It was Chicago's third win in four games against Nashville (23-9-3), which had a chance to replace the Blackhawks atop the division with a win in regulation. It looked like that might happen until three straight Chicago goals in the second erased a 3-0 lead for Nashville and Bickell's goal in made a 4-3 margin disappear.
"They have a lot of high-end talent all the way down throughout their lineup," said Predators forward James Neal, who scored twice. "They're going to make plays and they're going to have the puck a lot. The only way to beat that is you have to be on the offense more than them and you have to be physical with their skill guys."
Neal did his part. The goals he scored were his fourth and fifth this season against the Blackhawks, after a hat trick Oct. 23 in Nashville's 3-2 win. Neal has 12 goals and five assists in 18 games against Chicago.
Brad Richards, Andrew Shaw and Marian Hossa scored consecutive goals in the second to tie it 3-3 following Neal's first. Chicago defenseman Duncan Keith had three assists, and Bickell assisted on Shaw's goal for a two-point game.
Roman Josi and Craig Smith scored in the first period to give the Predators a 2-0 lead, but Chicago's resiliency was enough to drop Nashville's record to 8-2-0 when leading after one period and 14-2-0 when ahead after two.
"It's a big win," Blackhawks coach Joel Quenneville said. "Certain games will stick out at the end of the year that we'll say were a huge two points and tonight is probably leading in that category, as far as drama. Down 3-0 to a team that doesn't give up a whole lot, checks well, and then you have to pull the goalie and try to get an equalizer. Very resilient by our guys."
Nashville was left with a bitter taste again in a series that had three one-goal games and two that went past regulation. The Predators appeared in great shape with Rinne protecting a three-goal lead, but the Blackhawks countered with goals by Richards (10:33), Shaw (15:48) and Hossa, who scored at 17:43 on a power play.
Neal countered with his second of the game and 13th of the season to cap a power play, but the Blackhawks refused to let it be the game's last goal.
"We're a confident team," Shaw said. "We work hard for what we get. We go out there and we stick together, no matter what the score is, and we just keep plugging away."