Charlotte led 66-65 with 2:44 left in the third before Harden supplied nine points, including the final seven, during a 13-2 quarter-closing run that sent Houston into the fourth holding a 78-68 advantage.
The Bobcats got as close as five following Al Jefferson's turnaround hook shot with 2:14 to play, but Chandler Parsons and Patrick Beverley buried back-to- back 3-pointers for an 11-point lead with just over a minute remaining.
Parsons finished with 11 points, while Dwight Howard, who had missed Houston's last three games with a left ankle injury, posted a 10-point, 10-rebound double-double for the Rockets, who have won four straight games.
Kemba Walker paced the Bobcats with 22 points, while Jefferson supplied 20 points and 11 boards for Charlotte, which has dropped three of its last four games.
Swim Week Miami Beach 2014 [PHOTOS]