Houston never trailed and again used a balanced scoring attack with James Harden out for the third straight game with a foot injury.
The Rockets went up by 12 on John Jenkins’ 3-pointer early in the fourth quarter. Then Brooks outscored the Hawks 8-4 over the next 1½ minutes to extend Houston’s lead to 90-74. Houston shot almost 52 percent from 3-point range with Brooks and Garcia combining to make seven of Houston’s 14 3-pointers.
Paul Millsap had 16 points for Atlanta and Cartier Martin, who grew up in Houston, started in place of an injured Kyle Korver and had 14.
Chandler Parsons and Terrence Jones had 14 points each and Dwight Howard had 11 points and eight rebounds for Houston which improved to 11-5.
Al Horford scored 14 points and had eight rebounds as Atlanta dropped its third straight game.
The Rockets were up 77-67 entering the fourth quarter.
Harden was out with a sore left foot. Jeremy Lin started for Harden, who is averaging 24.2 points, 4.8 rebounds and 5.4 assists.
But Lin sustained a right knee bruise and left the game with about eight minutes left in the first quarter and did not return.
Brooks has been great in two of the three games with Harden out, scoring 26 points in the first before adding 21 on Wednesday.
Houston led by 11 points with about eight minutes left in the third quarter before Atlanta used an 8-2 run to get to 65-60. Millsap had four points in that span and Martin capped it with a jump shot.
The Rockets scored the next five points to push their lead to 70-60 with about four minutes remaining in the third.
Along with Korver (rib contusion), the Hawks were also without Shelvin Mack (sprained left ankle) and Lou Williams (right knee rehabilitation) who did not travel to Houston.
Korver was injured Tuesday night after extending his streak of consecutive games with a 3-pointer to 88. He needs one more to set the NBA record set by Dana Barros from 1994-96.
Atlanta coach Mike Budenholzer didn’t have any details on Korver’s injury and said he isn’t sure how long he’ll be out.
Houston jumped out to a 20-9 lead thanks to nine early points from Jones and was up 56-45 at halftime.
NOTES: Parsons has scored in double figures in 11 straight games. ... Coach Kevin McHale said before the game that Harden was feeling better on Wednesday and that he doesn’t expect him to be out for any extended time.