Okafor scored 21 points and had 16 rebounds and Wallace added 21 points to help Charlotte beat the injury-depleted Bulls 90-77 on Friday night.
Chicago played without its top two scorers, Ben Gordon (wrist) and Luol Deng (Achilles' tendinitis).
"They kind of struggled on the offensive end without those two key guys," said Wallace. "We tried to get them out of what they wanted to do and make it hard for them to run their offense without their key guys."
Charlotte held the Bulls to 37 percent shooting.
The Bobcats used a 15-4 run late in the fourth quarter to pull away. Leading 68-64, Okafor started the run for Charlotte with a three-point play and Wallace extended the lead to 83-68 on a jumper. Okafor shot 10-for-13 and blocked four shots, including a highlight block on rookie Joakim Noah in the first half.
The Bobcats won for just the third time on the road this season.
"They have been few and far between," Okafor said. "It feels good. We just had to come in and snag us one."
Andres Nocioni scored 25 points for the Bulls, who have lost five of their last eight games.
Interim head coach Jim Boylan questioned the motivation of the Bulls after the game.
"Our inconsistency showed again. It is difficult to understand why we have problems motivating ourselves. I know we are missing two of our main scorers. We should be able to step up and fill those voids with the guys we have," said Boylan.
Kirk Hinrich finished with 14 points and eight assists, but struggled with his shot. He was 6-of-16 shooting.
"I think it's a culmination of frustration. For whatever reason it kind of got the better of us right now. We were short-handed tonight, but at the same time we're a professional team. We have to go out there and just play better. Defensively, so inconsistent all year," Hinrich said.
Wallace's layup broke a 14-all tie and started an 11-0 Charlotte run late in the first quarter. Jeff McInnis' runner gave them a 25-14 lead early in the second quarter and the Bobcats led the rest of the way.
The Bobcats led 45-34 at the half. Okafor had 12 points and 12 rebounds in the half and Wallace added 10 points.