Houston center Dwight Howard did not play against his former team due to a right ankle sprain.
Carlos Boozer had 18 points with 11 rebounds for the Lakers, who have dropped eight straight games.
Los Angeles had not lost eight straight since March 14-27, 2005.
The Lakers will most likely be without the services of guard Kobe Bryant for the long term, as he recently suffered a torn right rotator cuff. He will be re-examined Monday before the team decides whether the guard needs potentially season-ending surgery.
With Bryant's absence, the Lakers will look to see more production out of Nick Young, but that wasn't the case on Sunday.
"I felt with his body language that I didn't want to play him," Lakers coach Byron Scott said of Young, who went 0-for-2 from the field in just under 8 1/2 minutes off the bench.
Harden netted seven points over the first five minutes and Houston went up 14-6 on Patrick Beverley's 3-pointer. Josh Smith hit a 3 late in the quarter to put the Rockets up 15 and they led 30-15 after 12 minutes. Harden notched 13 points in the opening frame.
Brewer's dunk gave Houston its largest lead of the first half, 42-23, with under eight minutes to play. Los Angeles chipped away at the deficit and trailed 52-36 at the break.
The Rockets sustained a generous lead throughout the third and led 80-60 entering the fourth. They led by as many as 25 in the final quarter, but the Lakers had one last gasp midway through the frame.
Jeremy Lin made two free throws to close a 10-0 run that brought Los Angeles within 89-78 with 5 1/2 minutes to play. Brewer countered at the other end with a 3-pointer to stem the momentum and Houston built another comfortable advantage to close out the game.
LA fell to 2-14 at home against the Western Conference ... Lin finished with 14 points in the loss ... The Lakers made 1-of-13 shots from beyond the arc ... The Rockets scored 21 points off 21 turnovers.