SALT LAKE CITY -- Mo Williams had just missed from 3-point range with 9.9 seconds left and the game tied against Western Conference nemesis San Antonio.

Instead of getting grief from his coach, Williams got another green light.

"Coach told me don't worry about it. You'll make the next one," Williams said.

He did.

Williams hit a 3-pointer at the buzzer to lift the Utah Jazz to a 99-96 victory Wednesday night that snapped the Spurs' five-game winning streak.

"It showed how much my teammates believe in me, showed how much the coaches believe in me," Williams said.

Now Utah players believe in their team, having knocked off the Lakers in Los Angeles on Sunday and a Spurs team that swept them out of the playoffs last season. It was the first time since 1997 that the Jazz beat both in back-to-back games.

"We're on a mission," Williams said. "We want to be good. We don't know our ceiling yet."

Paul Millsap led Utah with 24 points and 12 rebounds, Al Jefferson scored 21, and reserve Gordon Hayward added 19.

The Jazz trailed by eight with a little more than four minutes remaining. Williams' winning shot was his only 3-pointer of the night, and he finished with eight points on 3-for-9 shooting.

Spurs coach Gregg Popovich said Williams was able to get off the final shot because of a "huge" defensive error by Danny Green when the Jazz inbounded the ball with 6.7 seconds left.

"You got to make him drive with that amount of time," Popovich said. "That's why we put a bigger guy on Mo at the end so he couldn't get a shot off. You don't step off Mo Williams. What do you think he's going to do with two seconds on the clock? Instead of getting into him, he backed off. Huge defensive error."

After draining the shot, Williams looked up to make sure there was no time left, then took off running toward the other end of the court only to be mobbed by teammates.

"It was amazing," said Millsap, who grabbed the key offensive rebound after Williams' first miss. "It was a big win for us, a big win for our fans, a big win for our whole organization."

Tim Duncan and Tony Parker each scored 22 points to lead the Spurs, who swept the Jazz out of the playoffs in the first round last season and had won 11 of the previous 12 meetings.

Green's 19-footer gave the Spurs a 96-94 lead, and Millsap tied it with 40 seconds left.

While Duncan and Parker have been key for the Spurs, who entered Wednesday with an 11-2 road record, neither could make the shot at the end. Both missed long outside shots in the final 75 seconds as the Jazz improved to 9-1 at home.

"It was disappointing down the stretch," said Duncan, who also had 21 rebounds and six blocks. "Individually I made too many mistakes. I missed a jumper on the baseline I thought was down. Al (Jefferson) made a great play on the steal and layup. Just too many mistakes down the stretch that we couldn't recover from."

Williams hit the last shot but gave his teammates plenty of credit, especially Hayward, who took on guarding Parker the last four minutes.

"That was huge. That helped me," Williams said.

Before the game, Jazz coach Tyrone Corbin was excited for the matchup, especially after losing the first meeting 110-100 in San Antonio on Nov. 3.

Utah has had time to learn Corbin's system since then and time for its new acquisitions -- Mo Williams (trade), Marvin Williams (trade) and Randy Foye (free agent) -- to settle in.

Now the Jazz want more.

"We wanted to show everybody what we're capable of doing, and if we continue to play like that, we're going to shock the world. The sky's the limit for us," Millsap said.

Early on, it was the Spurs looking like the Spurs. They led by 10 twice in the first quarter as Duncan started strong inside and Green couldn't miss from outside.

The Jazz fought back behind a pair of 3-pointers from Foye, then got a spark from the energizing second unit. The highlight was a block from behind by Hayward as Gary Neal attempted to jam on the fast break.

The Jazz went on a 14-7 run to open the second quarter and took the lead on Millsap's 19-footer with 6:29 left in the half. Jefferson's three-point play on a fast break gave Utah a seven-point lead, and Millsap's layup capped a 7-0 run to put the Jazz up 53-44 at the break.

Millsap made his first five shots and was 6-of-7 at halftime with 13 points

The Spurs trailed by nine entering the second half, a stark contrast to the first game, in which Utah was down 19 at halftime but outscored the Spurs 35-17 in the third to get even before losing by 10.

On Wednesday night, the Spurs opened the second half with a 20-11 run, and Parker's fast-break layup tied it at 64 with 3:18 left in the quarter.

The teams were tied at 71 entering the fourth, but this time the Jazz made the big plays.

"We're headed in the right direction. We're starting to figure out how to win," Millsap said.

Game notes
The Jazz social media site proclaimed Wednesday "John Stockton Day" because of the number worn by the Jazz great. "It was fun watching him. If he was playing, I'd just be staring at him, and Karl (Malone)," Popovich said before the game. Stockton holds the Spurs' opponent record for most assists in a game, with 28 at Salt Lake City on Jan. 15, 1991. Corbin said Stockton was one of the "toughest competitors I played against and with as a teammate." Jazz CEO Greg Miller tweeted that he had a "nice visit with Stockton on this 12-12-12" and thanked him for all he's done. ... Jazz F Derrick Favors was back after missing the previous five games with plantar fasciitis in his right foot. He was averaging 9.3 points and 7.5 rebounds, and had a team-leading 32 blocks. He played (six minutes in the first half), and finished with six points and four rebounds.