Blake Griffin scored a season-high 36 points, while Chris Paul added 34 in a back-and-forth game that was never in double figures until the Hawks went on a 15-2 run at the end of the third quarter, sparked by Jeff Teague and Josh Smith.
Johnson clinched it with a pair of 3s, knocking down a desperation shot with 38 seconds remaining and the shot clock running down. He threw up a two-handed heave that somehow banked in, giving the Hawks a 103-96 lead.
In Oklahoma City, Kevin Durant scored 32 points, reserve Daequan Cook had all 19 of his points in the fourth quarter and Oklahoma City won its first game since top reserve James Harden took an elbow to the head.
Durant extended his lead in a tight NBA scoring race with the Los Angeles Lakers' Kobe Bryant despite sitting out the entire fourth quarter in a close game. Durant is averaging 27.97 points per game to Bryant's 27.86 with each having one game left.
Cook filled the scoring void, scoring Oklahoma City's first 14 points of the final period to put the Thunder ahead for the first time since the first quarter.
DeMarcus Cousins, who was allowed to play only after his 13th technical foul was rescinded earlier in the day, led Sacramento with 32 points.
In Boston, Sasha Pavlovic scored 12 of his of his season-high 16 points in the fourth quarter, leading a group of Boston reserves as both teams rested their top players.
LeBron James, Dwyane Wade and Chris Bosh were out for the Heat. Ray Allen, Kevin Garnett and Rajon Rondo didn't play for the Celtics.
Dexter Pittman had 12 points, James Jones scored 11 and Udonis Haslem grabbed 13 rebounds for the Heat, whose 25 turnovers were a season high.
Marquis Daniels finished with 13 points, Brandon Bass had eight points and eight rebounds for the Celtics. Boston's Paul Pierce finished with eight points. He started the game, but sat out the fourth quarter.
Miami's loss gave the Chicago Bulls the No. 1 seed in the East.
In Oakland, California, Golden State's Chris Wright was called for goaltending on Marco Belinelli's layup with 1.5 seconds remaining, giving New Orleans the win.
Greivis Vazquez blocked Charles Jenkins' layup to start a fast break in the final seconds. He pushed the ball ahead to a wide-open Belinelli, whose layup touched the backboard and was on its way down before Wright hustled over for the illegal swat.
In an odd scene, many Warriors fans were actually cheering for the Hornets.
Golden State has to finish in the bottom seven of the league after the draft lottery to keep its protected first-round pick, acquired by Utah in a previous trade. The Warriors are eighth worst in the league entering Thursday night's season finale at home against San Antonio.
In Salt Lake City, Paul Millsap scored 26 points and Al Jefferson went on a personal 8-0 fourth-quarter run as Utah clinched a Western Conference playoff spot.
The victory halted Utah's seven-game losing streak to the Suns, dating to March 2010.
Jared Dudley and Michael Redd scored 15 apiece for Phoenix, and Hakim Warrick had 12 for the Suns, who were without forward Channing Frye because of a shoulder injury.
The Suns won the season series but can't catch the Jazz with just one game remaining. Utah can still claim the No. 7 seed if Denver loses its final two games.
The Suns trailed 85-80 when Jefferson scored eight straight to put the game out of reach.
Jefferson finished with 18 points and 16 rebounds.
