Harden came in averaging 26 points, but only 5.4 assists and 4.4 rebounds, per game. He had four rebounds and four assists in the fourth quarter to reach the unique milestone.
"It means a lot to me, it's my first time ever," Harden said. "I was trying to make shots, trying to rebound, trying to find other ways to impact the game other than scoring."
The Rockets never trailed in the first half, repeatedly beating the Bobcats down the floor for easy baskets.
Charlotte held Harden to four points in the opening quarter and cut the deficit to 32-27 heading to the second.
Parsons swooped in for a putback dunk after Omer Asik missed a free throw early in the second quarter as the Rockets started stretching the lead again. Parsons already had 17 points with eight minutes left in the half, then zipped a cross-court pass to Harden for a layup and a 44-32 Rockets lead.
Houston had 16 assists on 24 first-half field goals and led 62-51 at the break.
Harden scored seven points, including a 3-pointer, in the first five minutes of the third quarter. He also earned a technical foul for mouthing off at a referee over a call, as the Bobcats began turning the tide.
"All the stuff we did really well (in the first half), we couldn't do in the third," Houston coach Kevin McHale said.
The Bobcats cut into the deficit with solid defense, holding the Rockets to only six field goals in the third quarter. Walker sank a 3-pointer and Taylor finished the quarter with a dunk to make it 79-77 heading to the fourth.
The Rockets took control again over the final nine minutes. Patterson sank a pair of 3-pointers and Harden finishing the Bobcats off with a layup and a long jumper.
NOTES: The Bobcats have lost their last eight games in Houston. ... Sessions scored at least 20 points for the fourth time in five games. ... Rockets F Carlos Delfino strained his right elbow in the second quarter and did not return to the game. ... The Rockets have scored at least 60 points in 18 first halves this season. ... Asik had 19 points and 15 rebounds for Houston.