In the extra session, Luol Deng gave the Bulls the lead on a three-point play with 2:52 to go, putting the Bulls up 102-101.
"The guys in there at the end did a great job of holding it together," said Dallas coach Rick Carlisle. "There was no panic in them when the Bulls got the lead late."
The Bulls were up 103-101 when Dallas rookie Dominique Jones hit a running layup and was fouled. He missed the free throw, but Ian Mahinmi got the rebound and was also fouled after making a basket. He hit his free throw and the five-point trip put Dallas up 106-103 with 26.4 seconds left to play in the extra session.
Deng missed a 3-pointer that could have tied the game and fouled Jones, who made two free throws to put Dallas up 108-103 with 19.7 seconds left.
Rose and Deng led the Bulls with 23 points apiece. Joakim Noah added 13 points, 15 rebounds, 5 assists and 3 blocked shots, but also committed 6 turnovers. Jones, who was celebrating his 22nd birthday, added 19 points for Dallas.
At the end of regulation, Dallas rookie Dominique Jones was fouled with 15.6 seconds left, but made only one of two free throws, leaving the door open for the Bulls.
After a timeout, C.J. Watson missed a 3-pointer. Brendan Haywood got the rebound for Dallas and got the ball to Jones, who was fouled. This time, he missed both free throws, giving the Bulls one last chance.
Rose inbounded to Deng, then cut off a screen and was left open on the left side. He sank his second 3-pointer of the game. J.J. Barea got a clean look at a winning 3, but his shot rimmed in and out, sending it to overtime.
"The shot was, I guess, a good shot," Rose said. "But we didn't win the game. That shot took it to overtime, but we didn't finish the game the way we were supposed to."
Omer Asik, the Bulls rookie seven-footer from Turkey, got his first start of the preseason.