Josh Smith added 16 points for the Hawks, who a night earlier scored 59 points at home against New Orleans.
Atlanta surpassed that total midway through the third quarter when it took control despite playing without injured starters Al Horford (sprained right ankle) and Marvin Williams (back). Coach Larry Drew also suspended reserve Josh Powell from the game for conduct detrimental to the team.
Drew said before the game they "burned the tape" of Friday's 41-point loss, but his players sure seemed to remember in a strange week that also included an impressive overtime win in Miami.
Playing with energy and poise, the Hawks shot 51 percent from the field a night after shooting 29 percent with Johnson leading the way.
After being held to nine points in the Hawks' lowest-scoring performance since moving to Atlanta 42 years ago, Johnson hit 12 of 18 shots and added five rebounds and five assists.
Wallace missed his first six shots and was held to seven points on 2-of-9 shooting. Jackson scored 10 points on 3-of-14 shooting while spending much of the night preoccupied with officials Eli Roe and Steve Javie. Roe gave him a second-quarter technical foul.
With Wallace and Jackson clanging shots, the Hawks stormed to a 74-63 lead on Johnson's deep 3-pointer late in the third quarter.
Wallace didn't get his first field goal until Charlotte trailed 82-67 early in the fourth. Bibby's 3-pointer with 5:44 left made it 91-77 and Atlanta didn't need a deep bench for only its third win in Charlotte in 11 tries.
Drew wouldn't say what Powell did a night earlier, saying only it was a "coach's decision" and it would be a one-game suspension. He didn't make the trip.
Drew also gave Zaza Pachulia his first start of the season ahead of Jason Collins at center a night after Collins was ejected in the third quarter for a vicious flagrant foul.
The Bobcats proved to be no match in a sluggish performance a day after power forward Tyrus Thomas underwent knee surgery.
Charlotte never got into an offensive flow in its 11th home loss, one more than all of last season. The Bobcats begin a six-game road trip Tuesday.
Notes: Drew said the issue with Powell is resolved. "Once we get back to Atlanta it'll be business as usual," Drew said. "There will not be a lingering or carry-over effect." ... It was Atlanta's sixth straight road win. ... Drew said Horford could return for Atlanta's next game Wednesday at Milwaukee. ... Williams' return remained uncertain. ... It was Jackson's ninth technical foul of the season. ... Coach Paul Silas said he doesn't expect the Bobcats to make any immediate moves to shore up the frontcourt depth. "As of right now we're going to leave it as is," he said.