The defenseman took a stretch pass from goalie Jacob Markstrom, moved into the zone and beat Chicago goalie Spencer Knight on the glove side.
Nemec had also tied the game 3-3 at 16:14 of the third period, tapping in a cross-ice pass from Stefan Noesen at the left post.
Jack Hughes had two assists for the Devils (12-4-1), who have won three of their past four, with each game going to overtime. Markstrom made 17 saves.
Chicago’s Connor Bedard scored to extend his goal-scoring streak to four games and his point streak to nine games (19 points; eight goals, 11 assists), tying his career long, set last season.
Knight made 33 saves for the Blackhawks (8-5-4), who had won three in a row. Nick Foligno and Louis Crevier each had two assists.
Bedard put the Blackhawks ahead 1-0 on a 5-on-3 power play at 18:35 of the first period. Bedard took a cross-ice pass from Teuvo Teravainen and scored on a one-timer from the left face-off circle.
Knight made saves on two breakaways in the second period, stopping Hughes at 11:57 and Hischier at 12:36.
Nemec tied the game at 19:45 of the second period, taking a drop pass from Hischier in the offensive zone, moving through the slot and scoring on a backhand. The Devils outshot the Blackhawks 14-3 in the period.
Landon Slaggert’s first goal of the season gave the Blackhawks a 2-1 lead at 3:05 of the third period. Slaggert tipped in Louis Crevier’s shot from the right point. The Blackhawks recalled Slaggert from Rockford of the American Hockey League earlier in the day to take the spot of forward Andre Burakovsky, who missed the game with an undisclosed injury.
Dawson Mercer tied the game again at 10:13 on a one-timer from the left circle, scoring short side while falling to one knee after taking a cross-ice pass from Hughes.
Sam Lafferty’s first goal of the season put Chicago back in front 3-2 at 13:34. Lafferty moved into the offensive zone, dodged Luke Hughes while going across the slot and scored on a backhand.
The Devils played most of the game without forwards Zack MacEwen and Cody Glass. MacEwen took a hit from Chicago’s Connor Murphy at 12:33 of the first period and did not return. MacEwen had missed 13 games with an upper-body injury before returning to play on Monday against the New York Islanders. After going into boards in the final minute of the first period, Glass came out for the second period but left for the locker room again after a shift.
