The Rockets frustrated the Clippers in the second quarter with Griffin and Jamal Crawford both drawing technical fouls for disputing calls against them.
"When that happens, it's a selfish act that doesn't make any sense, and it hurts the team," Del Negro said of the technicals. "I've got a lot of whining going on and a lack of urgency going on and it's disappointing."
The Rockets outscored the Clippers 48-26 in the paint, and the Houston bench outscored Los Angeles' reserves 39-31. Carlos Delfino scored 11 points and Patrick Beverley added nine for the Rockets' bench.
Garcia hit three straight 3-pointers in the first half to lead the Rockets with 13 first-half points. Houston led 55-50 at the break.
"If you look across the board, no one really did anything spectacular," Lin said. "But everybody played their role, did their jobs, and that's what you need when you're playing without your star player."
Asik registered his 30th double-double of the season with 13 points and 12 rebounds, adding two blocks.
Making his first NBA start in place of Harden, Rockets guard James Anderson scored seven points and added five rebounds, two steals and two assists. Rockets forward Greg Smith had nine points and eight rebounds, also in his first NBA start.
The loss dropped Los Angeles to fifth in the Western Conference as Memphis moved into fourth with a win over Minnesota.
Houston finished March with a 9-4 record after going 6-5 in February. On Monday, the Rockets host Orlando, while the Clippers host Indiana.
NOTES: Harden sprained his right ankle in a Feb. 12 road victory at Golden State and did not play the following game. A similar injury to the same ankle also caused him to miss a Dec. 10 meeting against San Antonio. ... Clippers forward Matt Barnes left the game in the fourth quarter with a left ankle sprain. ... Parsons, a University of Florida graduate, said he plans to attend Sunday's South Regional final between the Gators and Michigan, with a trip to the Final Four on the line.