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Carlos Boozer recorded 14 points and 14 rebounds in Game 4.
Okur bailed out Williams when he missed two free throws with 7.3 seconds left, then Okur made two from the line to seal an 86-82 win over the Houston Rockets on Saturday that put the Jazz up 3-1 in the best-of-7 series.
"Memo saved my butt. I ought to give him something. I ought to buy him a car or something,'' Williams said.
Okur had 18 rebounds, Carlos Boozer added 14 and the Jazz made up for some dismal outside shooting by controlling the lane.
"I tried to get myself going, stay active and mix my game up a little bit,'' Okur said. "The ball didn't fall for us, especially from the 3-point line tonight, but we were able to get the rebounds and get to the free throw line.''
Williams scored eight of his 17 points in the fourth quarter, starting an 8-0 run after Houston had trimmed a 16-point lead to just one with 10:39 left.
Houston got another break when Williams, one of Utah's better free throw shooters, missed both attempts, but Okur was there when the ball bounced off the rim and pulled down the biggest board of the night. Okur drew a foul, then sealed it with two from the line with 5.5 seconds to go.
The Jazz didn't make a 3-pointer - going 0-for-14 from beyond the arc. But they did play better inside than Game 3, which the Rockets dominated inside while cutting the series lead to 2-1, and can wrap up the series with a win Tuesday in Houston.
"We matched them on the inside play. That mattered a great deal more than what happened on the 3-point line,'' Utah coach Jerry Sloan said.
Tracy McGrady, who is 0-6 in playoff series, scored 23 points to lead the Rockets. McGrady was taunted with the chant "Over-Rated!'' when he went to the foul line late in the game. He scored just four points in another quiet final quarter.
Through four games, he has scored a total of 12 points in the final quarter - and seven of those came in a 94-92 win in Game 3 that revived the Rockets' hopes of going back to Houston with a possible 2-2 tie. Instead, it's a 3-1 deficit against a Utah team which won the first two games at the Toyota Center.
"It was more physical in this game. They were bodying me up and that's their game plan. I was still pushing through it, getting my shot,'' McGrady said. "We put ourselves in a great position in the fourth quarter.''
After Allston's 3-pointer cut the lead to two, Kyle Korver answered with two free throws for Utah to make it 84-80 with 12.5 seconds left. Then after Carl Landry put back an offensive rebound, Williams had a chance to seal it for the Jazz.
After his first miss, he still had a chance to put Utah back up by three. But he missed again, seeming to surprising everyone but Okur.
"That was huge. That was the play of the game right there,'' Utah's Matt Harpring said.
Andrei Kirilenko added an exclamatory block as the buzzer sounded and the Jazz left the court one win away from advancing. Kirilenko scored 11 and Ronnie Brewer had 12 points and two blocks as all five Utah starters scored in double figures.
After falling behind by 16 early in the third, Houston rallied to get within five points at the end of the period and continued to push early in the fourth to almost completely erase Utah's lead. Bobby Jackson and Landry hit two free throws each and Alston took a steal in all alone for a layup to cut the lead down to 68-67 with 10:39 left in the game.
"The one thing about this team is that they don't quit. They never give up,'' Houston coach Rick Adelman said. "It was a tough game. We just have to come back and regroup and get that game back in Houston.''
Williams took control for Utah by driving for two layups to start an 8-0 run. Harpring knocked the ball out of McGrady's hands, Williams bounced a pass to Boozer in the lane for an easy basket, then Korver made a 19-footer that put Utah back ahead 76-67 with 6 minutes left.
McGrady didn't score in the fourth until his layup over Boozer got Houston within 76-69 with 5:40 remaining. He had a chance to get the Rockets within two, but went 1-for-2 from the foul line twice.
McGrady also led Houston with eight assists and 10 rebounds, but the Rockets were outrebounded 48-41.
Notes: Jazz G Jason Hart missed the game with the stomach flu. ... The Rockets closed the first quarter on a 12-3 run to take a 23-21 lead into the second. ... After missing 13 free throws in Game 3, the Jazz improved Saturday by going 24-for-31 from the line. ... Battier scored 10 and Landry added 13 points for Houston.