The Thunder played without three-time NBA scoring champion Kevin Durant and Russell Westbrook, who were rested by coach Scott Brooks.
Serge Ibaka picked up the slack for the Thunder with 24 points on 10-of-17 shooting. James Harden, who won the NBA's Sixth Man Award last season, got a rare start and scored 13 points but was just 2 of 17 from the floor. Ibaka did not play in the fourth quarter.
Luol Deng scored 21 points and Joakim Noah finished with 15 points and 10 rebounds for the Bulls, who led by as many as 14 early in the third quarter.
Harden made two free throws and then found rookie Perry Jones for a dunk to cut the Chicago lead to 87-84 with 44.1 seconds left, but Boozer answered with a fadeaway jumper to put the Bulls up 89-84 with 34.4 seconds to go.
Richard Hamilton secured the game for Chicago with four free throws in the final 13 seconds. He finished with 13 points.
Jones scored 14 points in 20 minutes.
Boozer scored 13 points and Deng added 10 in the first half to help the Bulls take a 51-40 lead at the break.
After scoring eight points in the first half, Kirk Hinrich sat out the second half with a right groin strain.