With the lead slipping this time, Ben Gordon hit a jumper and Kirk Hinrich sank a 3-pointer from the corner to start an 15-2 run that gave Chicago a 94-72 lead.
Gordon scored 10 of his 17 points in the fourth quarter and Larry Hughes added 16 in Chicago's balanced attack.
New Jersey played the second half without starting point guard Devin Harris, who sprained his right ankle and limped off the court with 1:56 to go in the second quarter.
Vince Carter led the Nets with 22 points and Richard Jefferson finished with 21.
Chicago closed the first half with a 16-0 run to lead 58-34.
Both teams have losing records but are vying for the playoffs. The Nets were ninth and the Bulls 10th in the Eastern Conference entering play Tuesday night.
Thabo Sefolosha hit a pair of 3-pointers and Deng had a spectacular dunk on a pass from Hinrich to spur the 16-0 run by the Bulls that opened up the big halftime lead.
Chicago outscored the Nets 29-8 in the second quarter - New Jersey's lowest-scoring quarter of the season, thanks to 3-for-19 shooting in the period.
But Carter and Jefferson got the Nets back in the game, scoring 14 and 13 points, respectively, in the third quarter, as New Jersey cut the margin to 11.
Hinrich hit a jumper at the first-quarter buzzer and then added a 3-pointer and another basket to start the second quarter, sparking an earlier 12-0 Chicago run for a 34-26 lead.
