With the victory, in a game that will likely be a preview for the first round of the playoffs, the Jazz remain ahead of the Rockets in fourth place in the Western Conference standings.
Houston led 77-70 before Utah scored five straight points to get within two with 3:10 remaining. The teams exchanged a pair of baskets before a three-point play by Matt Harpring gave Utah an 82-81 lead with 1:35 remaining.
Boozer was fouled on a layup and made the free throw to extend the lead to 85-81 with 43 seconds left. Tracy McGrady pulled Houston within two on the next possession and the Rockets got the ball back after a miss by Boozer.
But Rafer Alston badly missed a 3-point attempt with about 10 seconds left and Houston was forced to foul. Okur made only the first to give the Rockets a chance to tie, but McGrady missed a 3-point attempt at the buzzer.
Yao Ming led the Rockets with 35 points and 16 rebounds, and also blocked four shots. McGrady added 20 points.
Deron Williams added 12 points, 11 assists and five rebounds for Utah. Gordan Giricek and Harpring added nine points apiece.
A basket by Giricek with 6:46 remaining got Utah within 71-70, but two free throws by Yao and two baskets by Juwan Howard stretched Houston's lead to 77-70 two minutes later. Howard finished with 10 points.
Houston used an 8-0 run to erase a four-point halftime deficit and take a 40-36 lead early in the third quarter. After hitting a pull-up 3-pointer that capped that run, McGrady ran to Yao and the two exchanged a handshake followed by a chest bump.
The Rockets led 58-49 after Andrei Kirilenko's block of McGrady's shot tipped it in. The Jazz then outscored Houston 10-3 in the final minutes of the third quarter to cut the lead to 61-59.
Utah led by as many as 10 points in the first quarter and was ahead 36-32 at halftime. Yao scored Houston's first 10 points and 18 of the team's first 22 as McGrady struggled, managing only three points in the first half until hitting two quick buckets just before halftime.