He led a late comeback for the second time in a week, converting a fourth-and-10 situation at his 20 with a completion to keep alive the Panthers' final possession, and their touchdown with 43 seconds left beat Miami 20-16.
The Panthers (8-3) overcame a 16-3 first-half deficit to extend their winning streak to seven games, their longest since 2003.
"We didn't play our best early on," Newton said. "We couldn't get it going. But we just find ways to win."
"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."
A backbreaker for Miami?
"That's when the tide shifted in our favor," Newton said.
Carolina then converted two third downs before Newton hit Olsen for the winning score.
Ryan Tannehill nearly connected with Wallace for a 60-yard score in the final seconds, but the pass fell incomplete at the goal line.
"That's a tough play," Tannehill said. "You're basically a hope and a prayer and get it out there."
Tannehill and Wallace earlier teamed up for a 53-yard touchdown and a 57-yard completion to set up a field goal.
Newton's interception led to another field goal by Miami, and he finished with a quarterback rating of only 60.6. But he was at his best with time running out.
Following the Panthers' uncharacteristically slow start, he led them 52 yards for a field goal in the final 61 seconds of the first half with no timeouts left, taking advantage of Miami's soft coverage to cut the deficit to 16-6.
Rivera's willingness to take chances paid off in the third quarter. From the Panthers' 41, Newton ran for 8 yards to convert a 4 and 1, and they went on to complete an 83-yard touchdown drive to make the score 16-13.
"They have been calling our coach Riverboat Ron because he likes to gamble," Newton said.
For the second game in a row, the Panthers' Luke Kuechly made a big play in the end zone that was disputed. He appeared to make helmet-to-helmet contact when he broke up a potential touchdown catch by Rishard Matthews, and an official threw a flag, but the referee determined there was no penalty and Miami settled for a field goal and a 16-3 lead.
While Tannehill threw for 280 yards, he was also sacked three times to increase his season total to 44, a franchise record. Carolina held Miami's running backs to 16 yards in 13 carries and shut out the Dolphins over the final 31 minutes.
"We were lazy in the first half," Carolina's Smith said. "We underestimated that team."
"We were a couple of plays away from winning," Tannehill said. "We've got to be able to make those plays. It's tough to win three-point games every week. When the defense is playing well like that, we've got to be able to score more points."
NOTES: Miami RB Daniel Thomas left the game in the third quarter with a left ankle injury. ... The Panthers had been 0-4 previously against Miami. ... Ted Ginn Jr. dropped a potential 50-yard catch playing in Miami for the first time since he left the Dolphins as a first-round bust following the 2009 season. ... The Dolphins announced their annual cycling event has raised $3.1 million for the University of Miami Sylvester Comprehensive Cancer Center.
Copyright 2013 by The Associated Press