Rose also had six assists, while Ben Gordon added 19 points and seven helpers for Chicago, which has won four of five and moved to 4-2 on its seven-game road trip. The Bulls will wrap up the trip Saturday at Dallas.
Tyrus Thomas ended with 15 points and 10 rebounds, while Joakim Noah added 16 points and nine boards in the Bulls' win.
David West and Peja Stojakovic each had 24 points for New Orleans, which has lost four in a row -- the longest skid of the Hornets' season. New Orleans played without All-Star guard Chris Paul, the team's leader in points, assists and steals. He suffered a groin injury in Monday's loss to Portland, and was considered day-to-day.
West also grabbed 14 rebounds, while Devin Brown contributed 17 points and seven assists in New Orleans' loss.
Chicago got off to a hot start, taking a 19-7 lead over the game's first five minutes. Thomas had eight points during the run, while Rose had six. The Bulls held the margin and led 31-20 going into the second quarter, during which they expanded their advantage.
The Bulls ended the half with a basket from Aaron Gray and two free throws from Gordon, and had a 62-44 lead at intermission. By the end of the third quarter, Chicago stretched its lead to 80-61, though New Orleans made a push to get back into the contest.
A 14-4 Hornets run in the middle of the final stanza ended with a Stojakovic three, which brought his team within 90-78 with 5 1/2 minutes left. A Ryan Bowen layup with four minutes left got New Orleans within 95-85, but the hosts didn't get their deficit to single digits.
Thomas followed Bowen's basket with a basket of his own, and Chicago cruised to the finish from there.