Newton led the Panthers on a 53-yard drive that resulted in a field goal from Justin Medlock and a 66-yard march that ended with a 2-yard scoring run by Jonathan Stewart.
The Carolina quarterback then threw a 9-yard touchdown pass to DeAngelo Williams at the end of an 80-yard drive for a 17-0 lead.
Newton completed 8-of-11 passes for 119 yards.
Miami rookie Ryan Tannehill was given the start amid speculation he will be the team's No. 1 quarterback at the beginning of the regular season. He was 11-of-23 for 100 yards without a touchdown pass or an interception.
The Dolphins closed within eight points on a 6-yard touchdown catch by Rishard Matthews with 3:23 to play and Miami got the ball back with 1:52 remaining.
Miami marched to the Carolina 4-yard line in the final seconds before the Panthers' Jeff Fuller intercepted a pass in the end zone thrown by Pat Devlin. Fuller then took an intentional safety to end the game.