Paul Millsap led the Hawks with 22 points and 11 rebounds, while Jeff Teague added 21 points. But Kyle Korver, with 12 points, was the only other Atlanta player in double figures.
Everyone else went 13 of 32 from the field.
"We're a new team," Carroll said, referring to Atlanta's massive turnover the last two summers. "This year is not going to make or break us. Just to be talking about making the playoffs is amazing."
The Hawks were up 42-38 with 9 minutes left in the second quarter after Mike Muscala knocked down a couple of free throws.
Chicago took control from there, clamping down defensively and scoring 16 of the next 19 points. The Hawks missed 12 of 13 shots, forced to settle mostly for outside jumpers and botching a couple of easy ones when they did get inside. Augustin capped the spurt with a brilliant hesitation move, freezing the Atlanta defenders before bursting through a gap for an easy layup.
The Bulls led 57-49 at the half and never surrendered the advantage.
Atlanta made several runs, only to have Chicago answer every one of them. With the Hawks down 93-87 and in possession, Taj Gibson swatted away Carroll's driving shot, the Bulls grabbed a loose ball and took off the other way, with Augustin sinking a 3-pointer that led to an Atlanta timeout.
It was another trey by Butler that finished off the Hawks — appropriate enough, since the Bulls went 12 of 25 beyond the arc. Augustin was 4 of 8 from long range, while Butler chipped in with three more.
In contrast to the Hawks, six players were in double figures for the Bulls, including Butler and Kirk Hinrich with 17 points apiece.
Atlanta has eight games left to pull out its seventh straight playoff appearance.
"This team is competitive," Elton Brand said. "There's no quit in us. We're going to play it out until the end."