Forte tallied a touchdown in a career-best performance and Hester's 69-yard score handed him the NFL record for most career punt-return TDs with 11.
He bested a mark held by Eric Metcalf, who played mainly for Cleveland and Atlanta in the 1990s.
The Bears (2-2) got another touchdown from their defense as D.J. Moore added a 19-yard interception return, helping to make up for a subpar day from quarterback Jay Cutler (9-of-17, 102 yards).
Carolina (1-3) lost despite another great day from rookie signal-caller Cam Newton, who passed for 374 yards with a score and rushed for two more touchdowns.
Olindo Mare connected on three field goals in the Panthers' defeat.