Meanwhile, Houston went cold while missing 16 of 20 field-goal attempts in the third quarter when momentum clearly switched squads.
"We played a lot harder defensively in the second half," Williams said. "We took a step forward as a team. We played crappy in the first half and we were able to turn it around."
And vice-versa for the Rockets, who fell to 16-21 with their fifth loss in a row.
"It's frustrating," said Houston forward Luis Scola, who topped the Rockets with 24 points and 10 rebounds. "We deserved to win this game, but we just didn't know how to close it."
The Jazz did, and the closing specialists offered an up-close-and personal-lesson on how to finish off teams.
Scola gave Houston an 82-73 lead with under six minutes to go when Millsap got started with a couple of free throws.
Raja Bell interrupted his shooting spree with a 3-pointer, but then Millsap scored seven consecutive points for the Jazz. With 1:29 remaining, he actually gave Utah its first lead in four games at 87-86 with an old-fashioned three-point play.
Millsap missed a potential game-winner near the end of regulation before scoring 12 of the Jazz's 14 points in the clinching overtime.
"You see the rim get bigger," Millsap added about his night. "And everything just starts going your way."
Fittingly, Millsap rebounded a Houston miss and ended up with the ball in his hands at the end of the game.
Millsap, who was referred to by teammates as Miss Bettye's son after his Miami heroics, got razzed in the locker room again while being called "The Legend" and "The Matrix."
For Millsap, it was infinitely better than being called inactive, which he was a few days earlier due to his bruised right hip.
Millsap played through that pain to score 20 in the loss at Memphis on Friday, and gutted through soreness again when the Jazz needed him the most Saturday.
"I had to block it out. I think I was a little bothered by it in the first half, not wanting to put too much pressure on it," said Millsap, who started this game 2-for-8. "The second half I just blocked it out and just tried to get out there and play. I just said, 'Get going, Paul.' You've got to hype yourself up every now and then."
The Jazz will take that kind of hype all they can get it.
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