Crabbe shot 7 of 13 and reached 20 points for the fourth time in six games and 10th time overall.
The Nets posted their first win since beating Philadelphia at home on Jan. 31.
DeMarre Carroll and rookie center Jarrett Allen each added 18 points as the Nets led by as many as 22 points and won for only the second time in their last 14 games since Jan. 21. Brooklyn outscored the Bulls 55-36 after halftime.
Reserve Joe Harris finished 15 points while the Nets won despite quiet nights from D'Angelo Russell and Spencer Dinwiddie, who combined for 11 points on 4-of-15 shooting.
Kris Dunn scored 23 points for the Bulls, who dropped their fourth straight and 13th game in the last 16 since Jan. 15. Rookie Lauri Markkanen added 19 points while reserve Bobby Portis finished with 12 as Chicago shot 35.5 percent, including 30.4 percent in the final 24 minutes.
The Bulls played without Robin Lopez and Zach LaVine, who were held out of the game. Chicago's Justin Holliday returned after sitting out the previous two games and shot 1 of 11.
The Nets held a 49-40 lead on a basket by Hollis-Jefferson with 2:24 left but gave up the final 11 points of the half. Chicago tied the game on a 3-pointer by Denzel Valentine with 35 seconds left and took a two-point lead at halftime on a mid-range jumper by Dunn with three seconds remaining.
Brooklyn scored the first nine points of the second half, but Chicago was within 58-56 on a 3-pointer by Dunn with 8:51 remaining. The Nets countered with a 15-4 run to take a 73-60 lead on Crabbe's 3-pointer with 5:55 remaining and carried an 84-70 lead into the fourth after scoring 35 points and shooting 63.6 percent in the third.
Brooklyn then finished it off late in the fourth with a 10-2 run that made it 101-80 on a 3-pointer by Carroll with 3:20 to go.
--Field Level Media
Chicago | Brooklyn | |
Kris Dunn 23 | Scoring | Allen Crabbe 21 |
Kris Dunn 4 | Assists | Spencer Dinwiddie 9 |
Denzel Valentine 13 | Rebounds | Jarrett Allen 9 |
Kris Dunn 4 | Free Throws Made | Allen Crabbe 3 |
Kris Dunn 2 | Steals | Allen Crabbe 1 |
Kris Dunn 2 | Blocks | Jarrett Allen 3 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Chicago | 87 | 35.5 | 6-23 | 15-23 | 17 | 56 | 7 | 8 | 14 |
Brooklyn | 104 | 44.4 | 16-42 | 8-8 | 31 | 48 | 9 | 4 | 15 |