The Panthers (7-3) scored 21 points in just more than eight minutes spanning both halves. That helped Carolina to a season-high point total against the NFL's lowest-scoring team.
Newton was 21 of 35 for 254 yards. He also rushed for 95 yards on five carries, including a 69-yard burst in the third quarter.
Carolina's 548 total yards marked a franchise record.
Panthers rookie running back Christian McCaffrey scored on a run and a reception and wide receiver Devin Funchess caught two touchdown passes, the last a 32-yarder from Newton with 8:20 remaining.
Running back Jonathan Stewart picked up a season-high 110 rushing yards on 17 attempts. Carolina racked up more than 200 rushing yards for the second game in a row, a first-time achievement for the franchise.
The Dolphins (4-5) lost their third game in a row.
Cutler was coming off his career-best game in terms of completion percentage (81 percent on 34 of 42 vs. Oakland), but he had that many incompletions by late in the second quarter at 8 of 16.
The Panthers went up 24-7 on the first possession of the second half when Funchess scored on a 28-yard screen pass from Newton.
Carolina got the ball back by stopping Miami's fourth-and-1 play from the Dolphins' 49. The Panthers cashed in with running back Cameron Artis-Payne's 12-yard touchdown run.
The Dolphins showed life when Kenyan Drake went 66 yards for a touchdown on a third-down run. The Panthers responded when Newton had his long run to set up his 2-yard scoring pass to McCaffrey.
The Panthers led 17-7 at halftime, in part because of a Dolphins gaffe late in the half.
Miami forced a punt and took over at its own 20-yard line with 47 seconds left, but Cutler's pass was intercepted by linebacker Luke Kuechly. With an unsportsmanlike conduct penalty tacked on, it gave Carolina possession at the Miami 20.
The Panthers converted on Newton's 7-yard touchdown pass to tight end Ed Dickson at the 19-second mark.
Carolina kicker Graham Gano opened the scoring with a 40-yard field goal with 1:50 left in the first quarter.
McCaffrey helped build the lead to 10-0 with a nifty move on a 4-yard touchdown run in the second quarter to cap a 12-play, 85-yard drive that consumed almost 6 1/2 minutes.
The Dolphins closed the gap with 2:12 left in the half when Cutler's flip pass to tight end Julius Thomas went for a 2-yard touchdown.
NOTES: Miami played in its NFL-record 83rd Monday night game. The Dolphins entered the game 41-41 in those outings. ... S T.J. McDonald made his Dolphins debut after coming off the NFL's suspended list. He had a would-be first-quarter interception overturned by video review. ... Panthers RB Christian McCaffrey reached 425 receiving yards for the season on the team's first possession, setting a season franchise record for a running back. ... Miami is back in action Sunday at home against Tampa Bay in a make-up of September's scheduled game postponed because of Hurricane Irma. ... The Panthers are off next weekend before a Nov. 26 game at the New York Jets.