The Hawks had six players score in double figures, including a season-high 16 points off the bench by Josh Powell, to overcome the loss of Johnson, the team's four-time All-Star and top scorer.
Rudy Gay led Memphis with 23 points.
The Hawks announced at the start of the game that Johnson will have arthroscopic surgery to remove a "loose body" from his right elbow.
CELTICS 99, TRAIL BLAZERS 95
In Boston, Ray Allen missed his first five 3-point attempts before hitting one with 10.7 seconds left to help the Celtics hold off a late charge by Portland.
Paul Pierce scored 28 points, Kevin Garnett had 17 points and eight rebounds, and Rajon Rondo had 10 points and 10 assists for the Celtics.
Wesley Matthews scored 23 points for the Blazers.
THUNDER 123, NETS 120 (3 OTS)
In Newark, N.J., Russell Westbrook capped a 38-point, 15-rebound, nine-assist performance by scoring all of Oklahoma City's 13 points in the third overtime, and the Thunder survived the absence of an injured Kevin Durant to beat New Jersey.
Brook Lopez led New Jersey with 28 points and 11 rebounds.
HEAT 97, PISTONS 72
In Miami, LeBron James scored 18 points in the final game before he heads back to Cleveland as an opponent, Dwyane Wade and Chris Bosh each added 16 and the Heat rolled past Detroit.
Greg Monroe scored 15 for the Pistons.
RAPTORS 127, WIZARDS 108
In Toronto, DeMar DeRozan scored 20 points, and the Raptors set a season high in points, beating Washington.
JaVale McGee had 21 points for the Wizards.