Jimmy Butler added 15 points with six rebounds for the Bulls, who remain tied with Toronto for the third seed in the Eastern Conference.
Robert Covington led the Sixers with 22 points, Jason Richardson went for 19 points and JaKarr Sampson chipped in 18.
Nikola Mirotic scored five straight points for Chicago to give them a 103-95 lead with 5 1/2 minutes to play in the fourth.
Hollis Thompson and Richardson each followed with a 3-pointer to cut the Sixers' deficit down to 103-101. Rose made a pair of baskets over the next minute around a Sampson layup that made it a four-point game.
The next point did not come until Butler converted a free throw with 1:25 left that made it 108-103, and Rose hit a jumper on the following possession as Chicago held off the lowly Sixers.
Aaron Brooks made a 3-pointer to end the first quarter and give the Bulls a 28-26 lead after 12 minutes.
Philadelphia opened the second quarter on an 8-0 run courtesy of two 3- pointers from Richardson. The Sixers led by as many as nine in the quarter, but they held a 53-52 edge at halftime. Chicago brought an 81-78 lead into the fourth.
The Bulls scored 19 points off 15 turnovers ... Gasol had a game-high three blocks ... Thomas Robinson had a team-high 10 rebounds off the bench for the Sixers ... Philadelphia will close out its slate at home against Milwaukee and Miami ... Chicago visits Brooklyn before ending the season with a home date against Atlanta.