The four overtimes tied for the third-longest game in NBA history. It was the ninth NBA game to go four OTs and the first since Phoenix beat Portland 140-139 on Nov. 14, 1997.
Al Jefferson finished with 28 points and 17 rebounds, and Paul Millsap had 25 points and 13 boards for the Jazz before both players fouled out in the final overtime.
Atlanta has won four straight and six of seven. The Hawks improved to 30-20 and moved one-half game ahead of Indiana for fifth place in the Eastern Conference.
Johnson ended the first quarter with 18 points after going 8 of 8 in the period. He missed eight of his next nine shots, including a potential game-winning runner with 3 seconds left in regulation, before hitting a 3-pointer that forced the third overtime.
With 16.9 seconds remaining in the fourth OT, Johnson’s 20-foot jumper over C.J. Miles gave the Hawks a 135-131 lead. Jeff Teague, who had 18 points and nine assists, added a pair of free throws with 13 seconds to go to make it 137-133. Johnson’s two free throws sealed the victory with 5.5 seconds remaining.
In Oklahoma City,   Kevin Durant had 28 points, nine rebounds and tied his season high with eight assists, Kendrick Perkins added a season-best 16 points and Oklahoma City opened a difficult stretch in their schedule by beating Miami.
The two title contenders opened the day tied for the second-best record in the NBA, three games behind the Chicago Bulls in the race for the top overall seed in the playoffs.
Oklahoma City had 13 steals and forced Miami into 21 turnovers that led to 28 points.
Dwyane Wade led Miami with 22 points but also committed a season-worst six turnovers. LeBron James had 17 points, seven assists and four turnovers.
DeJuan Blair added 19 points for the Spurs, who won for the seventh time in eight games and swept the season series with the 76ers despite being without Tim Duncan. With the Spurs playing three games in three nights, coach Gregg Popovich gave Duncan his second day off this season.
In Boston, Avery Bradley scored a career-high 23 points, and Paul Pierce added 21 points and eight rebounds to help short-handed Boston beat Washington.
Boston was without guards Ray Allen (ankle) and Mickael Pietrus (head injury) but still had plenty to hold off the struggling Wizards.
Rajon Rondo had 11 assists, while Kevin Garnett finished with 10 points and six assists for the Celtics, who shot 22 for 34 (65 percent) in the first half. In Minneapolis, Kevin Love followed up his 51-point game with 30 points and 21 rebounds to lead Minnesota over Denver.
Luke Ridnour had 25 points and six assists, and Wayne Ellington added 17 points for the Timberwolves, who have gone 3-6 since point guard Ricky Rubio was lost for the season March 9 to a torn ACL in his left knee.
In Cleveland,  Marcin Gortat and Markieff Morris scored 22 points apiece, and Phoenix never trailed against Cleveland.
Steve Nash added 13 assists for the Suns, who have won six of eight to get back into the Western Conference playoff race. Phoenix, which improved to 11-4 since the All-Star break, trail Denver and Houston by 1 1/2 games in the race for the final playoff spot in the conference.
Rookie Kyrie Irving scored 16 points for Cleveland, which has lost six of seven.
In Portland, Oregon,  Raymond Felton scored 24 points and LaMarcus Aldridge had 18, including a fadeaway jumper and two free throws that proved the difference in the final minute, leading Portland over Golden State.
Portland improved to 3-3 since Kaleb Canales replaced fired head coach Nate McMillan.
David Lee’s tip-in gave the Warriors an 87-86 lead before Aldridge hit a jumper to put Portland in front with 39.9 seconds left. Aldridge followed with two free throws.
In Los Angeles,  Rudy Gay scored 18 points and O.J. Mayo had 12 of his 16 in the fourth quarter, helping the Memphis Grizzlies avoid a winless road trip by beating the Los Angeles Lakers 102-96 on Sunday night.
Mike Conley added 13 points and Tony Allen had 12 for the Grizzlies, who squandered a 14-point third-quarter lead before pulling away in the fourth.
Andrew Bynum scored 30 points on 11-of-16 shooting to lead the Lakers. Kobe Bryant finished with 18 points after a slow start and Ramon Sessions also had 18 in his second start with Los Angeles.