There were 35 lead changes in the game with neither team able to build a cushion until the Rockets did in the final minutes.
Houston trailed by one with about 3 1/2 minutes to go before going on a 7-2 run to make it 110-106. Durant got things going in that stretch with a dunk and Jabari Smith Jr. added a three-pointer.
A layup by Tre Jones cut the lead to two, but Smith made a jumper before knocking down a three from the top of the key to extend the lead to 115-108 with about 90 seconds remaining.
Kevin Huerter made a layup for Chicago after that but a booming dunk by Durant left Houston up 117-110 with less than a minute to play.
Amen Thompson added 23 points for the Rockets and Smith scored 10 of his 18 points in the fourth quarter to help Houston snap a three-game skid.
Jones had a career-high 34 points for the Bulls, who lost for the fourth time in five games.
The Rockets led by six with about eight minutes left before the Bulls scored the next seven points, with three pointers by Isaac Okoro and Ayo Dosunmu, to take a 99-98 lead midway through the fourth.
Houston was just four of 20 on three-point attempts when Thompson hit one to put the Rockets back on top. But Matas Buzelis made one for the Bulls seconds later to give them a 102-101 lead.
Thompson made two free throws after that before a bad pass by Durant led to a basket by Buzelis that left Chicago up 104-103 with 3 1/2 minutes left.
Bulls: Host Utah on Wednesday night.
Rockets: Host the Thunder Thursday night.
