Johnson scored eight of his 35 points in overtime and the Hawks solved Portland's defense in time to beat the Trail Blazers 99-95 on Monday night.
The Hawks, who won at Portland on Nov. 3, swept the season series for the first time since the 1996-97 season.
Josh Smith had 20 points and 16 rebounds for Atlanta, which extended its winning streak to five with the victory in the matchup of division leaders. The Hawks' run includes a win at Boston.
"The last two years being in the playoffs has put this team in a totally different light," Hawks coach Mike Woodson said. "Now when they go on the court, they know they have a chance to win. ... It's kind of nice sitting on the top of the division."
The Hawks snapped Portland's six-game winning streak by rallying from deficits of 12 points in the third quarter and nine points, 67-58, at the start of the fourth.
"We were able to fight them off," Smith said. "Maybe three or four years ago we wouldn't have gotten the win."
Rudy Fernandez led Portland with 19 points, including a buzzer-beating 3-pointer at the end of regulation.
"The play was for me for the last shot and I made it," Fernandez said.
Atlanta enjoyed a 47-37 rebounding advantage. Al Horford overcame early foul trouble to total 15 points and 10 boards. Horford and Smith each blocked two shots.
The Hawks pushed the lead to 97-89 on two free throws by Johnson before Fernandez hit two 3-pointers in the final 12 seconds. Johnson had a combined 18 points in the fourth quarter and overtime.
"When my team needs it the most, that's when I want to come up big," Johnson said.