Viktor Arvidsson and Calle Jarnkrok scored on fluky plays in the first period for Nashville, which won for the seventh time in eight games and moved into a tie with Chicago for the fourth and final playoff spot in the Central Division. Pekka Rinne stopped 27 shots.
On the tiebreaking goal, Josi skated in and beat Subban from the slot after taking a feed from Eeli Tolvanen to cap a pretty passing series after Chicago failed to clear its zone.
Chicago, which dropped its second game in two nights to the Predators, has lost six of eight. The Blackhawks were limited once again for most of the game by defence-minded Nashville, which won 3-1 on Saturday.
With Nashville ahead 2-0, DeBrincat got Chicago on the board at 7:35 of the third when he whipped in a one-timer from the right circle after Rinne had lost his stick. Patrick Kane's pinpoint cross-ice pass set it up.
DeBrincat tied it with his 18th goal at 9:25. He sped around defenceman Dante Fabbro, cut across the crease and tucked in a shot to cap a nifty play.
The 38-year-old Rinne, Nashville's longtime No. 1 goalie, started for just the second time in seven games. The Predators' other goalie, Juuse Saros has gone 4-1-0 with a 0.81 goals against average and .977 save percentage in his last five games to backstop the their climb.
Nashville led 2-0 after the first period on goals that deflected in off skates.
Arvidsson was credited with opening the scoring 4:43 in. He jumped on a loose puck behind the net after Subban couldn't handle it. The puck ticked of defenceman Calvin de Haan's skate and into the net.
Jarnkrok made it 2-0 with his 10th goal with 1:30 left in the period. Mattias Ekholm circled behind the net, spun and fired from the left circle The puck caromed in off Jarnrkok's foot at the edge of the crease as de Haan tried to tie him up.
Rinne's 368 wins are the most for any Finnish goalie. The 2018 Vezina Trophy winner has played his entire NHL career with Nashville. He made his NHL debut and earned his first career victory on Dec. 15, 2005, versus Chicago.
He scored a goal against the Blackhawks last season, firing a 185-foot shot into an empty net to cap a 5-2 win at Chicago on Jan. 9, 2020.
Blackhawks C Dylan Strome didn't play because of the birth of his first child.
Nashville F Filip Forsberg missed his second straight game with an upper-body injury.
Predators: Host Dallas on Tuesday in the first of a two-game series.
Blackhawks: Host Carolina on Tuesday in the first of a two-game set.