The eight wins already surpasses Charlotte's seven wins all of last season.
"When you go through an entire month without a win, it really eats at you," Dunlap said. "It's especially hard for our young guys who need to build confidence."
Ramon Sessions scored 11 first-half points to give Charlotte a five-point advantage at the break. He finished with 15.
The Bobcats shot over 50 percent from the field in the first half, but struggled from the free throw line, hitting just six of 15 attempts to keep Chicago in the game.
The Bulls began intentionally putting Charlotte on the line in hopes of mounting a comeback, to no avail.
"They weren't shooting free throws well," Thibodeau said. "You're just searching for anything that can get you going."
The Bobcats finished 21 of 38 from the stripe — worse than mediocre, but enough to get the job done.
Chicago has lost three of its last four.
"We're in a funk right now, we've been up and down this season," said Taj Gibson, who had eight points and nine rebounds. "Tonight, we let down a lot on defense and we just have to find our way out of it."
Notes: Bulls G Kirk Hinrich was ruled out before the game due to "a compilation of things," according to coach Tom Thibodeau. He is considered day-to-day. ... Thibodeau said he was "sad" to hear about the firing of Chicago Bears head coach Lovie Smith. "You hate to see anyone lose their job, but that's the nature of the beast," he said. ... Bobcats F Michael Kidd-Gilchrist (scratched right cornea) did not play after being poked in the eye during a 98-95 loss to New Orleans on Saturday.