The Rockets cut the deficit to 64-61 after three quarters before Harden re-entered the game and calmly led the Rockets all the way back.
Asik pumped his fist and confidently nodded his head as he trotted back down the court after Harden dropped in his final basket.
With the Rockets up 85-84, Barea drove the lane, but was stripped by Carlos Delfino.
Harden scored on the ensuing possession.
Chandler Parsons had 12 points, and Delfino had 11.
McHale also was close with Michael Stephenson, a 42-year-old man who died of pneumonia last week and couldn't walk or talk after being born with cerebral palsy.
Stephenson and McHale became friends in the early 2000s, and Stephenson appeared in the Timberwolves' 2002-03 team photo.
The team held a moment of silence for Stephenson before the game.
NOTES: Rockets forward Chandler Parsons injured his left knee Tuesday in a win over the Bulls, but played more than 35 minutes on Wednesday. ... The announced attendance was 20,340, the third-largest crowd in Target Center history.