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' streak also 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," said Fernandez, who added two more 3s in overtime.
Portland had won four straight road games, holding each opponent under 85 points, before falling to the Hawks in the last game of its trip.
"We played good here but probably the road trip is very long and we were tired," Fernandez said. "But it's a positive for us."
"It's disappointing because we had a big lead and we didn't do a good job of taking care of the ball and defending," Roy said. "But they beat us up on the inside and dominated the paint."
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.
"They won the game how they've been winning the game, in the paint," Portland coach Nate McMillan said. "I thought the defense did a better job of keeping them out of the paint, but we didn't finish. We didn't finish the play with rebounding the ball."
Johnson started overtime with two quick field goals. Following a basket by Horford, Johnson scored again for a 93-87 lead with 1:42 remaining. Greg Oden, who had 11 points and seven rebounds, had Portland's only basket in the first 3 minutes of OT.
The Hawks pushed the lead to 97-89 on two free throws by Johnson before Fernandez had two 3s 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.
Johnson hit two 3-pointers in the fourth, each tying the score.
Johnson's drive with 14.8 seconds remaining in regulation gave Atlanta an 83-82 lead. He pushed the lead to three with two free throws, but Fernandez hit a fallaway 3 to send it to overtime, connecting over Horford.
The Trail Blazers pushed the ball inside to Oden in the opening minutes and quickly sent Horford to the bench. Horford drew his second with 3:08 remaining in the first quarter and did not return in the first half.
Horford's Florida Gators beat Oden and Ohio State to win the 2007 NCAA championship at the Georgia Dome in Atlanta, adjacent to Philips Arena.
F Travis Outlaw is out indefinitely and was not with the team after suffering a stress fracture in his left foot in Portland's win in Charlotte on Saturday. ... Johnson had his 60th career game with 30 or more points. ... The Hawks are 5-0 at home.