Rookie Ayo Dosumnu had 15 points and played a key role in the late rally as Chicago snapped a two-game losing streak.
The Nets had played Sunday in Toronto and appeared to run out of gas late.
Brooklyn held a 78-76 edge entering the final quarter. Aldridge hit a pair of free throws to open the scoring in the fourth, but Chicago responded with 13 straight points to take command.
DeRozan had back-to-back jumpers to tie the score at 80 and Dosunmu put Chicago back on top with a free throw. Dosunmu then converted a three-point play on the next possession to make it 84-80.
Chicago stretched the lead to 89-80 before Durant scored the Nets’ first field goal of the fourth with 7:46 remaining. Alex Caruso countered with a 3-pointer to stretch the lead to double digits for the first time at 92-82.
Nikola Vucevic added 11 points and 13 rebounds for Chicago, which had dropped back-to-back games to the Philadelphia 76ers.
Unlike the previous three games, Chicago got off to a fast start and took a 35-27 lead after the first quarter. The Bulls were up 47-45 late in the second quarter before Brooklyn took control with 10 straight points, sparked by two 3-pointers by Joe Harris, for a 55-47 lead.
The Nets led 57-51 at halftime, with Durant and Aldridge leading the way with 15 points apiece.