With Utah leading by seven in the fourth quarter against the reigning NBA champs, the Jazz forward released a 22-foot jumper that wasn't close.
The Jazz came right back to the unfazed Williams and his back-to-back 3-pointers sparked Utah to a 94-89 win over the Miami Heat.
''I can't think of a bigger win than this one,'' said Williams, who scored 23 points.
Trailing 87-79 after Williams' shots, the Heat used a 10-4 run to draw within two points after Ray Allen made a 3 from the corner with 46 seconds to play.
Rookie Trey Burke, who had 13 points, rose up and drained the clutch 19-foot jump shot to beat the shot clock and Gordon Hayward's free throw clinched the win for the Jazz, who have beat the Heat at home three straight times.
Burke has said he hit the classic rookie ''wall'' that often plagues first-year players after they've played 35-40 games. Shooting just over 30 percent the past three games, his teammates and coaches have encouraged him to keep shooting.
''They come to me and tell me to play with confidence. 'Don't think about it. Just play freely.' That's what I did tonight,'' said Burke, who had a penchant for big shots as the AP Player of the Year at Michigan last season.
Dwyane Wade had 19 points for the Heat, who missed their last four shots from the field to thwart their comeback bid. LeBron James was 4 of 13 from the field for 13 points, his lowest scoring total since he had 13 points in a 104-88 win over Atlanta on Nov. 19.
''There's nobody that can stop LeBron from scoring the basketball, but we tried to slow him down collectively as a team and I think we did pretty good,'' Williams said.
Hayward nearly had his first triple-double with nine points, 11 assists and nine rebounds, while often guarding Wade and James. Richard Jefferson had 14 and Alec Burks had 12 points for the Jazz, who snapped their four-game losing streak in front of a frenzied crowd.
James subbed in with 7:54 to play and his team trailing 77-70 and the Heat looked poised for a comeback as they also reached the penalty with 6:51 to play. But James missed his only two field goal attempts of the fourth quarter and was 2 of 4 from the line.
The young Jazz, who entered the game with worst record in the Western Conference, relied on their two veterans down the stretch until Burke's big shot.
Williams, who averages 9.9 points, has scored 67 points in his last three games and made 5 of 8 from beyond the arc in this one.
After his air ball, Williams made a pair of 3-pointers - the last shot just beating the shot clock after Jefferson dove to the floor to gather a loose ball and flip it to Utah's hot hand.
''He just found somebody open and I was able to get away from Chris Bosh. I just threw it up there and was able to beat the clock and it went in,'' Williams said.
Once the Heat turned up the defensive pressure, the Jazz were often scrambling to get any shot they could muster late in the clock. When the ball ended up in the hands of Williams and Jefferson, who had seven in the final period, good things happened.
''I can't say enough about their focus and desire to help this young group grow. And their play has been great, gives us a chance to be competitive every night,'' Utah coach Ty Corbin said of his veteran forwards.
James has averaged 31.3 points and 7.8 assists per game in his last four on the road as the Heat have found their offense, shooting better than 50 percent.
''It was just one of those games where offensively we were out of rhythm and you try to win on the defensive end,'' said James, whose team dropped to 27-2 when holding opponents under 100 points this season.
The four-time MVP also had scored 30 or more in six straight trips to Salt Lake City, averaging 33.5 points while hitting 57.7 percent from the field, but didn't ever get things going in a contest that snapped the Heat's three-game winning streak.
''We didn't shoot the ball well like we are capable of doing,'' James said. ''We had some great looks, including myself, some really open looks.''
Even after a couple nights off, the Heat started sluggishly and the Jazz ran around and through them for a 32-18 lead in the first quarter. The Jazz had 11 assists in the opening period and shot 62 percent.
James gave the Heat their final lead in the opening moments of the third quarter at 54-52, but Utah controlled the game the rest of the way.
''It seemed we were always in the right place at the right time tonight,'' Hayward said.