Chicago has won five straight and with help can move up to the fifth seed in the Eastern Conference. The Bulls (40-41) are tied for sixth with Indiana and Milwaukee and a half-game behind Washington. Chicago hosts Toronto on Wednesday in its regular-season finale.
"Our goal is to be the highest seed we can. That is our motivation to move up," Hinrich said. "We have a shot to finish .500 for the season and improve our seeding. We have a lot to play for."
Hinrich was 15-for-20 from the free-throw line but missed several free throws at the end of regulation. However, he hit five straight to extend Chicago's overtime lead to 108-102 with 44.1 left.
Hedo Turkoglu had 32 points, including a 3-pointer with 3.2 seconds left in overtime, and nine rebounds, while Dwight Howard added 22 points and 14 boards for Orlando, which saw its eight-game winning streak end.
Jameer Nelson chipped in 15 points and seven assists and Keyon Dooling scored 12.
Orlando finishes the season Wednesday night at Indiana.
Hinrich hit a 20-footer with 22.2 left in regulation to give Chicago a 96-95 lead. After a timeout, Turkoglu drove the lane and drew a foul, making the second of two free throws to make it 96-96 with 13.2 seconds left.
Ben Gordon missed a 16-foot jumper as the clock ran out at the end of regulation.
Nocioni scored seven points in a 14-4 fourth quarter run that gave Chicago its first lead of the game, 81-80, with 8:11 left after two Hinrich free throws.
"We're happy because we're playing really, really well," Nocioni said. "We're creating and taking open shots and we're running the offense."
The Magic didn't score for almost three minutes in the fourth until Dooling hit a three-pointer from the wing, making it 83-83 with 6:33 to go. Neither team led by more than two points after the bucket until the extra period.
"They deserved to win," Magic coach Brian Hill said. "They played hard, they made big shots when they needed them and it probably wasn't one of our better offensive efforts from the standpoint of getting real good ball movement and taking care of the basketball."
Luol Deng had 22 points and 11 rebounds and Gordon added 18 points for the Bulls.
The Magic honored former player and current Bulls coach Scott Skiles before the game with a video tribute and the unveiling of a banner. Skiles received a plaque but didn't speak to the crowd. The guard played five seasons with Orlando and remains the franchise leader in assists with 2,776. He averaged 13 points and seven assists over 384 games with the Magic.
Orlando led by 16 points in the third quarter after a Turkoglu 3-pointer, but again went scoreless over the next 3½ minutes. Chicago rattled off a 9-0 run to draw within seven before Nelson stopped the burst with a long jumper just before the shot clock ran out.
Turkoglu and Tyson Chandler were called for double technicals with 1:08 left. Chandler fouled out at 3:09 in overtime with four points and four rebounds. ... Nocioni was shaken up at 3:25 in the fourth quarter after taking a forearm to the midsection from Howard. ... Former University of Miami guard Guillermo Diaz,
who is forgoing his senior season to enter the NBA draft, was in attendance. ... Chicago wore red jerseys and blue shorts from the 1946-47 Chicago Stags team and Orlando sported pinstripe uniforms from its inaugural 1980-90 season as part of the NBA's Hardwood Classics Nights. ... Chicago took the season series from Orlando 3-1.