James Harden finished with 18 points for the Rockets, who shot 55 percent (46 of 83) and hit half of their 3-point shots at 11 of 22. Greg Smith and Carlos Delfino each scored 13.
Gordon Hayward had 13 of his 21 points in the second half and Al Jefferson and Randy Foye each scored 20 for Utah. The Jazz lost despite shooting 51 percent (48 of 94) overall and going 11 for 20 from 3-point range.
Omer Asik had 14 points and 12 rebounds for Houston. He briefly left the game after taking an elbow from Hayward, but returned for the final minutes.
The Rockets have won five straight home games. Utah has dropped three of its last four road games.
Utah took advantage of Houston's sloppiness at the start to build an early lead. But Utah's shooting tapered off with the reserves on the floor early in the second quarter.
Houston led 58-49 at the break after hitting 23 of 39 shots (59 percent) in the first half, its best percentage for a half this season. Parsons went 5 for 7 for 13 points and Asik made all four of his shots for 11 points in the half.
Hayward sank a 3-pointer and scored seven points in the first six minutes of the third quarter, and the Jazz rallied to tie it. He was whistled for an offensive foul when he elbowed Asik on a drive. Asik came out of the game and walked to the locker room, pressing a towel to his face.
Hayward sank another 3 with 3:26 left in the third to put the Jazz up 75-74. He scored 11 points in the quarter and made all four of his shots, then dunked an alley-oop pass from Earl Watson early in the fourth.
Delfino, back after missing seven games with a groin injury, hit a 3-pointer to tie it at 88 and Parsons converted a three-point play after finishing a fast break to put Houston back on top.
The Rockets hit three 3-pointers early in the fourth quarter to stretch the lead to 10, but the Jazz answered with a quick 9-0 spurt to cut the deficit to 105-104. Both teams had their starters on the floor for the last six minutes, including Asik for Houston.
Patterson sank a corner 3 for a 112-109 lead with just over four minutes left. Patterson reached 20 points for the fourth time this season. Harden drove for a one-handed dunk a minute later.
Mo Williams and Jefferson scored in the lane, but Asik put back an offensive rebound despite a horse-collar foul by Foye and sank the free throw for a 121-113 advantage with 1:20 left.
The Jazz, who are 3-9 on the road, but 6-0 at home, return to Utah Monday night to face the Los Angeles Clippers.