Bynum's shot came with 15.7 seconds remaining in regulation and Jonas Jerebko sank a key basket with 50.5 seconds to go in the extra frame for the Pistons.
Prince finished with 24 points, Jerebko added 18 and Bynum logged 17 for the Pistons, who notched their third win in four contests.
The Bobcats, meanwhile, fell for the seventh straight time despite 20 points from Mullens.
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