Muncy ended up with $249,914 in season earnings, just $8,540 more than Jesse Wright and $35,772 more than Cody Wright, a two-time world champion who finished fourth this year.
"I felt like I rode decent ... and I'm just tickled to death," said Muncy. "The goal is to come here and ride all 10, and it worked out."
Asked if he felt the Wright brothers were double-teaming him, Muncy laughed.
"That's every rodeo," he said. "If you're in a rodeo and you see them there, you know they're going out for first and they do it quite often. So it's just an honor to be here and ride with them."
Meanwhile, Payson's Kaycee Feild capped off a record-shattering run in bareback by winning Round 10 with a score of 87.
Feild, who clinched his first world championship Friday night, set records for 10-ride average, NFR earnings and single-season earnings.
"It's awesome," Feild said. "I'm just so happy. I prepared myself to come down and dominate, but I didn't really expect this. ... I'd just like to thank God for how it all turned out."
Feild's win also clinched the Ram Top Gun Award, given to the individual who wins the most money at the NFR. He entered the final round with a $581 lead over Jesse Wright and rides away in a new Ram pickup truck.
In other events involving Utahns, Santaquin's Wesley Silcox won the bull riding with a 90.5, Payson bull rider Steve Woolsey didn't score, and Ogden's Jody Sheffield didn't place in the barrel racing.
How Utahns fared at the National Finals Rodeo
Listed are event, final world standing, earnings at the NFR and season earnings:
Kaycee Feild, Payson Bareback 1st $179,327 $319,986
Jody Sheffield, Ogden Barrel racing 8th $49,904 $118,218
Wesley Silcox, Santaquin Bull riding 7th $32,019 $133,149
Steve Woolsey, Payson Bull riding 14th $24,807 $95,028
Cody Wright, Milford Saddle bronc 4th $66,202 $214,142
Jesse Wright, Milford Saddle bronc 2nd $160,962 $241,374