Ellis, the NBA's third-leading scorer entering the game, was held to 12 points, and Curry managed just nine points as each player missed nine of 13 shots. The Warriors stayed close into the fourth quarter behind Dorell Wright's career-high 32 points.
That wasn't enough to offset the Hawks' 51 percent shooting and 31 assists on 44 field goals.
"We knew we would have our hands full with Curry and Ellis, but I think we did a pretty good job with them," Hawks coach Larry Drew said. "We did a good job contesting their shots, but then Wright made shots. Sometimes you give something up to stop something else."
The same thing happened to the Warriors. Once they gave more attention to Smith and Horford, guard Mike Bibby shook free for 10 points in the third quarter.
Bibby finished with 15 points, and Joe Johnson scored 16 while passing Lenny Wilkens for No. 10 on the franchise scoring list.
"I'm a big fan of Lenny," Johnson said. "It's an honor and a privilege. It says a lot not just about me, but about this team and organization and where we've come to where we are now."
The Hawks led by as many as 12 points in the third quarter. The Warriors twice got within six early in the fourth quarter, but the Hawks finally slowed their scoring and pulled away.
Horford's alley-oop dunk on a pass from Smith and Smith's 3-pointer pushed the Hawks' lead to 92-81 with less than five minutes left. After Ellis made a 3-pointer to cut the Hawks' lead to 94-86, Bibby answered with a 3-pointer to help hold off the Warriors.
Wright's 12 points over the final nine minutes of the second quarter helped Golden State cut a 12-point lead to 52-47 at halftime. Curry opened the second half with a 3-pointer, but the Hawks responded with a 9-0 run that made the score 61-50.
It took a while longer for the Hawks to take control for good because the Warriors kept pouring in 3-pointers and Wright was all over the court. He had seven points and four rebounds in the third quarter as the Hawks led only 78-69 entering the final quarter.
"I can tell when the guys are at home they feel like they can turn it off and on when they have to," Drew said. "We have to respect every opponent because on any given night you can be beat."
Hawks forward Marvin Williams left the game in the third quarter after falling to the court and suffering a bruise to his lower back.
"I got up quick, but when I tried to walk back to the bench, it locked up on me," he said. "I will see how it feels [Thursday]."