Josh Smith scored 30 points and pulled down 12 90.
Zaza Pachulia also had a double-double with 10 points and 14 rebounds for the Hawks, who went 3-1 on a four-game homestand. Jeff Teague and Kirk Hinrich added 16 and 10 points, respectively.
"We played the way we're capable of playing," Smith said. "It feels good to be able to get a win against a high-powered offensive team like the Oklahoma City Thunder."
Kevin Durant ended with 35 points and eight boards for the Thunder, who had a seven-game winning streak snapped. Russell Westbrook tallied 25 points.
The Hawks led for a majority of the first quarter and took a 27-24 lead into the second.
With the score tied at 79 with 7:29 to play, the Hawks went on an 8-0 spurt. Layups by Teague and Pachulia preceded a pair of Smith slams, giving the home team an 87-79 lead with 4:42 to go.
Durant made a three-pointer and two free throws around Smith's trey to cut the gap to 92-90 with 1:48 left.
Smith made 1-of-2 from the line and added a hook shot to give the Hawks a 95-90 margin with one minute remaining.
Durant and Westbrook each missed shots around a Smith turnover. Teague was then called for an offensive charge, giving Oklahoma City another chance. Durant missed a three-pointer this time around.
Smith made two foul shots with 24.1 seconds left to make it a seven-point contest.
"Tough one for us," Durant said. "Their a good team, they played hard. They ended up with a better score than us."
With the score tied at 27 early in the second, Atlanta went on a 13-4 run to create some distance. Vladimir Radmanovic made a three-pointer during the burst, which Smith capped with two free throws for a 40-31 margin with 5:35 left.
The lead reached 11, 49-38, on a pair of Marvin Williams free throws. But the Thunder ended the half on a 9-4 flurry to cut the gap to 53-47.
Down by eight, 68-60, with 5:48 to go in the third quarter, Oklahoma City put together an 11-2 run to take the lead. Cole Aldrich's two free throws made it 71-70 with 1:24 left.
Radmanovic and Jannero Pargo each made three-pointers to give the Hawks a 76-75 edge after three periods.
The Hawks snapped a four-game skid against the Thunder...Atlanta guards Joe Johnson (left knee) and Willie Green (back) missed the game...The Thunder went 24-of-29 from the foul line, while the Hawks went 15-of-22 from the charity stripe...Oklahoma City turned the ball over 21 times, leading to 22 Atlanta points...The Thunder had 10 blocked shots.