Rodon held the No. 1 national seed Tar Heels hitless into the fifth inning. He allowed five hits and struck out eight.
It was the sophomore left-hander's second straight dominating performance against the Tar Heels. The result was more satisfying this time. Three weeks ago he allowed one hit and struck out 14 in 10 innings but got no decision in a 2-1, 18-inning loss in the Atlantic Coast Conference tournament.
The Wolfpack's first CWS appearance since 1968 will continue Tuesday when it plays either LSU or UCLA. The Tar Heels (57-11), in Omaha for the sixth time in eight years, are one loss from elimination.
Brett Williams, Bryan Adametz and Logan Ratledge had two hits apiece for the Wolfpack (50-14), with Ratledge driving in two runs out of the No. 9 hole.
NC State and Carolina, whose campuses are 28 miles apart, were meeting for the 285th time in baseball but never on this big a stage.
Rodon thrived on it.
He opened by walking Chaz Frank on four pitches, then retired 14 straight batters before Brian Holberton singled up the middle on a first-pitch fastball with two out in the fifth inning.
Rodon got help from a defense that turned two double plays. The first one ended the seventh inning after the Tar Heels had a runner at second with one out. The second came after Holberton singled leading off the eighth.
The Tar Heels broke through in the ninth, with Frank singling leading off and Landon Lassiter following with an RBI double.
Emanuel was nothing like he was two years ago at the CWS when he threw a four-hit shutout against Texas as a freshman.
Emanuel failed to make it out of the third inning for the second straight start, and the Tar Heels tied a CWS record by using eight pitchers.
The junior left-hander was down 5-0 when he was pulled Sunday after allowing two doubles and two singles to the final five batters he faced.
The Houston Astros' third-round pick now has an 11.40 ERA in five NCAA tournament appearances, having given up 19 runs in 15 innings.
Emanuel had pitched at least into the seventh inning in 14 of his first 15 starts, and he has logged more career innings (340) than any junior in program history. Carolina coach Mike Fox has been criticized in some quarters for his handling of Emanuel in the NCAA tournament. He made a 51-pitch relief appearance in regionals two days after throwing 124 pitches in a start.
He was tagged for four runs on seven hits in 2 1-3 innings in the super-regional opener against South Carolina, and he got no decision in the Tar Heels' 6-5 win. He threw just two pitches while earning his first career save in the super-regional clincher.
The Wolfpack and Tar Heels have split four games this season and could meet again at the CWS.