Atlanta had a 75-62 advantage going into the fourth quarter but the Trail Blazers produced the first 14 points of the period.
Johnson then scored five of the 11 points during the Hawks' surge that brought them their fourth straight victory, all on the road. Portland has lost four out of five.
Johnson finished with seven rebounds, five assists and two steals. Josh Smith had 17 points and 11 rebounds for the Hawks.
Jamal Crawford paced Portland with 22 points. LaMarcus Aldridge scored 20 to go with 11 rebounds.