Irving entered Saturday sixth in the NBA with 28.5 points per game but sat with a right shoulder injury. Brooklyn was just fine without him with Dinwiddie stepping into the starting lineup.
Zach LaVine scored 36 points, but Chicago shot 35.2% from the field, 23.1% from 3-point range and committed 20 turnovers.
Joe Harris had 22 points and eight assists for Brooklyn, which snapped a three-game skid. The short-handed Nets are also without Caris LeVert, who's recovering from right thumb surgery.
The lead changed hands five times in the fourth, and Brooklyn pulled ahead for good on Dinwiddie's dunk with 8:01 remaining.
Chicago briefly got within three points with just under 3 minutes left, and Lauri Markkanen hit a fading 3-pointer to make it 113-111 with 8.8 seconds remaining. But Harris made two free throws and the Bulls never got the ball with a chance to tie it.
Wendell Carter Jr. added 18 points and 14 rebounds for the Bulls, who trailed by double digits early before using a 23-5 run in the second quarter to take the lead.
Chicago led from then until the fourth quarter but allowed 43 points in the final period.
Nets: Coach Kenny Atkinson said Irving's status for Monday's game against Indiana is unclear. . Six Nets scored in double figures.
Bulls: Coach Jim Boylen said he expects F Otto Porter Jr.'s return from a left foot sprain to be a matter of weeks, rather than months. He doesn't think Porter will need surgery.
Nets: Return home to face Indiana on Monday.
Bulls: Host Milwaukee on Monday in the second of a four-game homestand.
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Jordan puts the full denial on White
Coby White heads to the rim and DeAndre Jordan sends his shot into the stands.