Hamilton tied it 3-3 at 14:32 with a shot from the right circle that went in off the far post.
Hughes then put New Jersey in front 4-3 at 14:51 on a partial breakaway, skating past Chicago defenseman Alex Vlasic before shooting over the glove of Spencer Knight. Hughes added an empty-net goal at 19:29 for the 5-3 final.
Connor Brown and Simon Nemec also scored, and Jake Allen made 27 saves for the Devils (38-33-2), who were coming off a 5-2 loss at the Carolina Hurricanes on Saturday but are 3-1-0 in their past four games and 6-2-0 in their past eight.
Frank Nazar scored twice for his first multigoal NHL game, and Anton Frondell had two assists for his first multipoint NHL game for the Blackhawks (27-34-13), who have lost three in a row. Knight made 35 saves.
Ilya Mikheyev put Chicago ahead 1-0 at 4:19 of the first period. Allen went behind the net to retrieve a dump-in, but he lost track of the puck in his skates, which allowed Frondell to steal it and quickly pass out front to Mikheyev for a shot into an open net.
Brown tied it 1-1 on a power play at 11:15 by deflecting a shot-pass from Luke Hughes in the slot.
Nazar put the Blackhawks back in front 2-1 at 13:11. He buried a one-timer near the right post off a cross-crease backhand pass from Ryan Donato, who was near the left post.
Nemec tied 2-2 at 15:48 of the second period, scoring through traffic from the top of the right circle after Dawson Mercer won a battle for the puck along the goal line.
New Jersey outshot Chicago 16-5 in the second period.
Nazar gave the Blackhawks a 3-2 lead during a 5-on-3 power play at 10:51 of the third period. He finished a no-look, cross-ice pass from Connor Bedard with a one-timer from the left circle.
