Stoudamire scored 14 points, including a game-closing five straight, as the Grizzlies beat the Jazz 80-72 on Saturday for their fourth straight victory.
"I've made a lot of big shots in this building throughout my career," said Stoudamire, who made a 3-pointer as the shot clock expired with 45.8 seconds left in the game.
After the Jazz cut the lead to 75-72 with 1:10 to play, Stoudamire beat the shot clock and then made two free throws with 37.6 seconds left to lift Memphis (7-3) to its best start in the franchise's 11-year history.
"Damon's shot was huge with the shot clock running out," Memphis coach Mike Fratello said.
With points tough to get near the basket, the Grizzlies went outside and Miller scored 15 of his 18 points in the second half. Miller, who made three 3-pointers and shot 7-of-11, was demanding the ball and his teammates were setting screen after screen to get him open.
"Mike Miller was huge once he got it going," Fratello said.
"It was a tough game, one we re very happy to pull out," said Pau Gasol, who had 14 points, seven rebounds and six blocked shots.
Jazz rookie Deron Williams matched his career high with 21 points for the second straight game and added 10 assists but got little help as Utah (4-7) lost its fifth straight.
Thanks to Miller s sharpshooting, Memphis built an 11-point lead in the fourth quarter before Williams hit two 3-pointers to start a 10-2 run. However, Shane Battier ended the rally with a three-point play and the Jazz missed six field goals in the final minute.
"We made a big run getting it down to three, but we couldn t capitalize and get over the hump. We just couldn't get stops for a long period of time," said Williams, who scored or assisted on Utah's final 14 points.
The Jazz, who rank near the bottom of the league in field-goal shooting and turnovers, shot 37 percent and rarely got an uncontested shot. Utah has yet to reach 100 points this season.
"You've got to learn to be tough in certain situations and not turn the ball over and get a decent shot every time you come down the court. You can't bail out on screens," Utah coach Jerry Sloan said.
Fratello became the second-winningest coach in franchise history (47-29), passing Sidney Lowe (46-126). Hubie Brown is the leader with 83 wins.
"Fratello has his team playing together," Stoudamire said. "I think all our new guys are blending in here and everybody's pulling for one another and that's the biggest thing in the NBA."
The Grizzlies, who lost their first 17 games against Utah, have won four straight against the Jazz.
Sloan picked up his folding chair and nearly launched it onto the court after a foul call midway through the fourth quarter. He got a technical. ... The game capped a back-to-back set for the Jazz, who opened a second consecutive four-games-in-five-nights stretch with Friday's loss to Phoenix. ... Utah plays nine of its next 11 at home.