Andre Iguodala led Philadelphia with 24 points, his fifth straight game with 20 or more points, but said Miller was the star.
"He hit about four big shots down there," Iguodala said of the fourth-quarter run. "He hit some big shots and created a spurt."
Samuel Dalembert also scored 19 points with 10 rebounds, seven blocked shots and no fouls.
"That's pretty hard to do," Cheeks said.
Steven Hunter had 15 points and Kyle Korver added 11.
Josh Smith led Atlanta with 21 points and 10 rebounds for his third straight double-double. Marvin Williams had 18 points.
Johnson had nine assists but was held to 16 points, nine below his average.
The Hawks are 7-5 when Johnson scores 30 or more points and 8-22 in other games.
"I thought they played harder than us and they wanted it more," Johnson said. "Give them credit. They played a great game."
Atlanta couldn't build on the momentum of back-to-back road wins at Boston and Orlando. In each game, the Hawks won after trailing by more than 10 points, but they couldn't repeat that winning formula against the Sixers.
"It's very frustrating," Woodson said. "When you come home and play in front of your fans, you want to play well. For some reason, from the beginning to the end, we just didn't have it. ... I thought their energy level was a lot higher than ours."
Added Atlanta's Josh Childress, who had 11 points: "It's a game we could have and should have won."
Philadelphia, meanwhile, rebounded from Friday night's 105-97 loss to Cleveland in which the Sixers were outscored 33-19 in the fourth quarter.
"We bounced back tonight," Cheeks said. "This is a good step in the right direction."
The Sixers, 9-13 since trading Iverson, have won three of their last four games.
Added Iguodala: "Tonight I don't think we played great but we just played good enough to win."
Each team was playing for the second straight night, but only the Hawks appeared tired early.
The Hawks appeared to be consistently a step behind on defense as the Sixers shot 58 percent in the first quarter and 54.2 percent for the game.
"When we got tired, we became very individual players offensively," Woodson said. "I don't think we had any effort defensively at all."
The Hawks never led and the only tie was at 2. A fallaway jumper by Hunter gave the Sixers a 23-14 lead, and Philadelphia's biggest first-half lead was 12 points at 53-41.
Notes: Philadelphia is 2-0 against Atlanta this season. ... Philadelphia outscored Atlanta 28-20 in the final period. ... Iguodala has 14 games with 20 or more points. The Sixers are 8-6 in those games. Twelve of the 14 games have come in the last 23 contests. He set a career high with 34 points on Wednesday night in a win over Cleveland.