Newton completed 21 of 35 passes while Jonathan Stewart ran 17 times for 110 yards to spark the host Panthers.
Newton completed 21 of 35 passes while Jonathan Stewart ran 17 times for 110 yards to spark the host Panthers, who improved to 7-3, just behind first-place New Orleans (7-2) in the NFC South division.
It's the first three-game win streak for Carolina since a 14-0 start in 2015.
"Being able to do this at home made it a little bit more special," said Christian McCaffrey, who ran for one touchdown and caught a pass for another. "Our offense is at our best when we're in a rhythm and flowing."
The Dolphins fell to 4-5, missing a chance to match Buffalo for second in the AFC East with their third loss in a row.
Carolina's Graham Gano kicked a 40-yard field goal in the first quarter to open the scoring and the Panthers jumped ahead 10-0 on McCaffrey's 4-yard touchdown run, which capped a 12-play, 85-yard march with 7:05 remaining in the second quarter.
Miami answered with a 10-play, 75-yard touchdown drive that ended on Jay Cutler's 2-yard pass to Julius Thomas, pulling the Dolphins within 10-7.
But Carolina's Luke Kuechly intercepted a Cutler pass and four plays later, Newton tossed a 7-yard touchdown pass to Ed Dickson with 19 seconds remaining in the second quarter and the Panthers seized a 17-7 half-time lead.
Newton flipped a screen pass to Devin Funchess and he rambled into the end zone on a 28-yard touchdown reception only 3:10 into the third quarter.
After Carolina's defenders stopped Miami on downs to force a turnover, the Panthers struck again with Cameron Artis-Payne rushing 12 yards for a touchdown as the Panthers stretched their lead to 31-7.
The Dolphins responded with their longest play of the season, a 66-yard touchdown run by Kenyan Drake. The play snapped Miami's club-record nine-game touchdown run drought.
But Newton led the Panthers to answer quickly, his 69-yard run to the Miami 18-yard line setting up his 2-yard touchdown pass to McCaffrey four plays later as Carolina stretched the lead to 38-14.
Newton connected with Funchess on a 32-yard touchdown pass with 8:20 remaining but Miami answered with Cutler finding Jarvis Landry on a 9-yard touchdown pass with 4:13 to play.