Hester's 69-yard touchdown punt return was his 11th in 182 career punt returns, breaking a tie with Eric Metcalf for the league record.
Hester also had a 73-yard kickoff return against the Panthers but was forced out of bounds by Carolina kicker Olindo Mare.
"It feels good," Hester said Sunday of his touchdown. "I knew my teammates were thirsting for a return, and I'm just glad and pretty honored to be on a team like this where we have 10 other guys out there that want a return just as bad as me."
Hester now has 39 punt returns of 20 yards or more in his career, which is the most in the NFL since the veteran entered the league in 2006. He is also the all-time leader for combined touchdowns on kick returns with 15.
Hester also surpassed Dante Hall (2,261) for 23rd in career punt return yards. Hester now has 2,300 punt return yards.
Hester won the award for the 10th time, the most ever by a return specialist.
ESPNChicago.com's Michael C. Wright and information from The Associated Press was used in this report.