Newton's scoring strike to Olsen came with 4:20 remaining for the Panthers (1-2), who logged their first win after losing to Arizona and Green Bay to start the season.
Newton went 18-of-34 through the air for 158 yards and has now racked up 1,012 yards in his first three NFL games -- the first rookie ever to gain that much yardage over his initial three contests.
Fellow rookie signal-caller Blaine Gabbert completed 12-of-21 passes for 139 yards, one touchdown and an interception in his first career start for the Jaguars (1-2).
Gabbert took the field after Luke McCown was benched.
Maurice Jones-Drew compiled 122 rushing yards and 45 receiving yards for Jacksonville.