Brown scored a season-high 15 points and grabbed nine rebounds, and Ben Wallace added 11 points and seven boards for Chicago, which has won nine straight over the Hawks.
Six players scored in double figures for the Bulls, who stopped a two-game skid. They host the Mavericks on Thursday before the defending NBA champion Heat come to town Saturday.
Brown said the Bulls know their recent play won't even keep them competitive against their upcoming opponents.
"We're talking about it. We know that's not going to get it done," he said. "There is no way we're going to get away with playing that type of basketball on that trip, so we tried to tighten up and play consistent and get a lot better."
Chicago took control in the third quarter, scoring nine consecutive points to open an 18-point cushion. Andres Nocioni made two free throws at the end of the third, then converted a three-point play to give the Bulls a 77-59 lead early in the fourth.
"Every game is important for us right now, especially in this building," Wallace said. "We have to force teams to come in here and work extremely hard to beat us."
The Bulls outscored the Hawks in the paint 40-26.
Joe Johnson led Atlanta with 29 points and Marvin Williams added 22. The Hawks have lost three straight after winning three in a row.
"This was a tough, ugly game," Johnson said. "We never really got into a rhythm. It was tough for them, too, but they got in a stretch where they made a little run."
Nocioni hit a 3-pointer and Ben Gordon made a three-point play to give Chicago a 62-51 lead with 4:03 left in the third quarter. Gordon scored 10 points in the period and finished with 12.
Nocioni had 14 points off the bench for Chicago.
Josh Smith scored 16 points for the Hawks after being fined $25,000 by the NBA on Monday for making obscene gestures to the crowd as he left for the locker room following a second-quarter ejection Saturday night in a loss at Charlotte.
The Bulls led 41-37 at halftime behind 11 points from Brown. Williams led Atlanta with 14 points on 7-of-8 shooting. He was 2-for-4 in the second half.
Wallace and Brown combined for 17 of Chicago's 27 points in the first quarter.
"The coaches have wanted more activity down low," Brown said.
Before the game, Bulls general manager John Paxson spoke to reporters about potential trades. Paxson didn't confirm or deny discussions with the Grizzlies involving a potential trade for forward Pau Gasol, but he did discuss what an asset Gasol would be to the Bulls without mentioning Gasol's name. "We need a guy to score like that. We need somebody with length that could score around the basket, take some pressure off of Ben (Wallace)," Paxson said. ... The Hawks played without guards Tyronn Lue and Speedy Claxton. Lue sat out with a strained groin and Claxton missed his sixth straight game with a sore left knee. Lue has missed 16 games this season with the groin injury.