Andrei Kirilenko added 27 points to help spark the Williams-less Jazz, who won for the first time since Jan. 14.
Before the game, Millsap admitted his thumb was throbbing.
After the Jazz's much-needed victory, however, he broke into a broad grin.
"Before a game before and after the game you feel everything. A lot of pain. A lot of knickknacks," Millsap said.
"But during the game, you try to suck it up. You don't really feel it too much when you are out there running. And that's what I did. I didn't feel it when I got on the court."
According to coach Jerry Sloan, Millsap enjoyed "a terrific game. He just kept playing. He just kept rebounding. That's one good thing about him he'll fight back."
In this game, Minnesota kept fighting back, too.
The Timberwolves' only lead was 3-2 in the opening minute.
Utah led by eight late in the first quarter, nine late in the third and 90-79 with 10:49 remaining.
But Minnesota never let the Jazz get comfortable.
In fact, Utah owned a tenuous 103-100 lead when Millsap took a pass from Earl Watson, who finished with 13 assists, and buried a 15-footer that finally allowed the sellout crowd of 19,911 to exhale.
"They made a good push," Watson said. "This is the NBA. Everybody is talented. At the same time, we're at home and we know what we're capable of doing.
"You never panic, but you get a sense of urgency a controlled sense of urgency that's not a panic point. So we stayed in it, kept pushing the pace and extended our lead."
Defensively, the Jazz didn't stop the Timberwolves until it mattered most.
Minnesota managed one field goal in the final 7:39 and committed three of its 25 turnovers in the final 2:09.
"Just active everybody had active hands," said C.J. Miles. "And we talked. We had a sense of urgency to close that game out. We knew we had to get a couple of stops.
"The big guys did a good job showing on the pick-and-roll, so they couldn't turn the corner, and we closed out to the shooters at the end."
The Jazz went into the game without Williams, who was scratched from the lineup after being unable to grip the basketball at the morning shootaround.
Millsap and Bell played despite their injuries, and Okur was lost in the first half when he strained his back.
Still, the Jazz survived, in part, because Watson helped them get off to a fast start.
Utah jumped to a 13-4 lead.
Watson had four points and seven assists in the first quarter, when the Jazz made 15 of 26 shots.
"Earl was terrific pushing the ball and getting us into the open court," Sloan said.
Said Watson: "I don't think they expected us to come out and run. We got a lot of points in transition, and it took a lot of pressure off our half-court offense.
"During the losing streak, every shot seemed so monumental because we were always trying to get back into the game. But not tonight" he added.
R IN SHORT • Paul Millsap scores 30 points and the Jazz snap a six-game losing streak.
KEY MOMENT • After leading by 11 in the fourth quarter, Millsap hits a jumper with 46 seconds left to make it 105-100.
KEY STAT • The Jazz limit Minnesota to 6-of-20 shooting in the fourth quarter. They also force 25 turnovers.