The Panthers (8-3) overcame a 16-3 first-half deficit for their seventh win in a row, their longest streak since 2003.
"It may not be pretty," Newton said, "but at the end of the game we get that three-letter word, and that's gorgeous."
Newton hit Greg Olsen with a 1-yard pass for the winning score to cap a 12-play drive. Carolina also rallied past the New England Patriots with a late drive last Monday.
The Dolphins (5-6) fell to 2-2 since tackle Jonathan Martin left the team and the team's bullying scandal began to mushroom.
"We've got to make plays at the end when it counts," receiver Mike Wallace said. "We've got to have a killer instinct. I don't think we have it that well right now. We've got to do a better job of putting teams away."
The Panthers trailed 16-13 when their winning drive began at their own 20 with 4:13 left. With only one timeout remaining, they went for it on fourth down, and Newton threaded a pass between two defenders to Steve Smith for a 19-yard gain.
A backbreaker for Miami? "That's when the tide shifted in our favor," Newton said.