The Grizzlies outscored the Hawks 42-18 in the third quarter to quickly erase the big lead Atlanta opened in its preseason opener.
"We don't match up with the Hawks," Grizzlies coach Lionel Hollins said, noting that the Grizzlies have lost seven of the last eight regular season meetings between the two teams, "so for us to get a win in any kind of way, I'm happy."
Randolph also had eight rebounds for Memphis (1-1). Acie Law scored 19 points, 11 in overtime, and had five assists for Atlanta. Law was 10 for 10 from the free throw line.
Marvin Williams had 18 points and 10 rebounds, and Josh Smith added 15 points for the Hawks. Point guard Jeff Teague, who played the entire 5-minute overtime, finished with 20 points and six assists.
"Sometimes when you're practicing and doing it, it looks pretty well," Hawks coach Larry Drew said. "And when you get in the game situation and the lights come on, you start to forget a little bit. You don't make reads. Which I expected."
The Hawks had a 10-0 lead in fast-break points at halftime. The final total was 17-16 for the Grizzlies.
Atlanta gave up 17 points on eight turnovers in the third quarter, and 34 points on 26 turnovers for the game.
The Hawks have exercised Teague's 2011-12 option. Teague, the 19th overall pick in the 2009 NBA draft, played in 71 games last season, averaging 3.2 points and 1.7 assists. Hawks G Jamal Crawford (back), G Mo Evans (knee) and G Pape Sy (back) were out. Grizzlies C Hamed Haddadi (personal reasons) and G Greivis Vasquez (right ankle surgery) were not with the team.