John Salmons added 20 points, Ben Gordon 18 and Brad Miller 14 off the bench for the Bulls, who snapped a seven-game road losing streak and won its third straight game.
Kevin Durant led the Thunder with 28 points and Jeff Green added 18 for the Thunder, who saw its four-game home winning streak come to an end.
New Orleans jumped out to a 29-22 edge after one stanza and held a 56-51 advantage after 24 minutes of game action. In the third, Chicago pounced with six consecutive points almost midway through to claim a 65-64 edge. Rose hit the first two jumpers and Gordon converted another for the one-point advantage.
The edge grew to five points, 69-64, after a Salmons bucket in the lane and Tyrus Thomas' thunderous slam. Thomas notched a double-double with 12 points and 11 rebounds on the game.
The Thunder responded with seven straight points of their own moments later, taking a 75-74 edge after Chucky Atkins' layup. Rose and Joakim Noah followed with buckets in the paint for an 80-74 margin after three.
In the fourth, Chicago's last field goal came courtesy of Rose with 4:45 to go. The rookie's bucket handed the visitors a 97-88 lead, but the Bulls lived at the charity stripe from there.
Nick Collison, who tallied 12 points with 13 rebounds, banked home an easy bucket and Russell Westbrook, who added 15 points, slashed into the lane and converted for a 99-96 deficit with 56.8 seconds to play.
The Bulls again came up empty, and Durant had an opportunity at a tie, but his contested three-pointer from the right corner bounced off the rim. Thomas made all four of his free throws down the stretch to seal the victory.