The Rockets ended the game on a 14-4 run, during which the Bulls missed 11 consecutive shots.
Harden was able to play only 17 1/2 minutes in Houston's loss to Utah on Monday, but went 8-of-14 with five steals during 42 minutes against the Bulls.
Houston snapped a three-game skid and handed the Bulls their third straight loss. Chicago is 1-3 on a five-game road trip that wraps up Friday in Milwaukee.
Patrick Patterson scored 20 points for Houston while Chandler Parsons had 18 points and a career-high 13 rebounds.
Nate Robinson paced Chicago with 21 points, Luol Deng had 19 points and Carlos Boozer grabbed 15 rebounds. The Bulls have lost three straight for the first time dropping 10 in a row midway through the 2009-10 season.
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