Drew Gooden added 18 points and 11 rebounds for the Bulls, who have won four of their last six overall. Derrick Rose chipped in 16 points and seven assists in the win.
Chicago forward Tyrus Thomas left the game with 7:27 remaining in the second quarter with a concussion and did not return.
Marcus Camby tallied a career-high with 27 rebounds to go with his 19 points for the Clippers, who saw their season-high three-game win streak ended. Zach Randolph poured in 30 points and Al Thornton 20 in defeat. Baron Davis had 16 points and 12 helpers while Eric Gordon scored 17 points.
Randolph scored the first three points of the extra frame for a 109-106 Clippers lead with 3:39 left in OT.
Luol Deng, though, answered with a pair of jumpers to give Chicago a 110-109 lead with just over a minute to play.
On the following Clippers possession, Randolph shouldered Nocioni and got called for the offensive foul. The Bulls took over with 51 seconds showing on the clock.
With 42.6 ticks left, Rose drove the lane and poured in a layup before adding a free throw for a three-point play for a 113-109 Chicago lead.
Larry Hughes stole the LA inbounds pass on the next play, and the Bulls held on for the victory.
The clubs played to a 26-26 tied after the first quarter but the Bulls pulled away, 56-47, at the half.
Camby's layup sparked a 12-0 LA run the Clippers used to tie up the game, 63-63. Thornton's dunk capped the surge just prior to the midway point of the third stanza.
The teams traded baskets and Davis' three-pointer gave the Clippers an 80-77 lead heading into the final 12 minutes.
Mardy Collins' layup gave the Clippers a five-point lead early in the fourth.
Nocioni's baseline jumper brought the Bulls within 92-90 right around the six-minute mark.
Down by four, the Bulls scored eight straight points to take the lead, 98-94, with a shade under four minutes left in the game.
Randolph's layup and jumper gave the Clippers a 100-99 lead, and Camby blocked Rose's layup offering and grabbed the ball before LA called a timeout with 1:06 showing on the clock.
Following the stoppage in play, Camby had a tip-in off a Randolph miss, and it was 104-101 just inside the final minute.
Driving the lane, Randolph was fouled with 25.1 ticks left. He hit 2-of-2 to make it 106-102 in the Clippers' favor.
On the ensuing inbounds, Gordon took a pass, dribbled around the top of the arc and unleashed an off-balance, leaning three that tickled the twine. He was also fouled on the shot and sunk the free throw to tie it up at 106 with 20.5 seconds left.
Davis took the pass at the top of the arc and threw a pass to Thornton, who dribbled around the right wing and launched a shot that caromed in and out of the rim.
Chicago got the ball back with .6 seconds remaining but was unable to get a shot off and the teams headed for overtime.