The freshman left-hander pitched the first complete-game shutout at the College World Series in five years in a 3-0 victory that eliminated Texas on Monday.
Emanuel limited the Longhorns to four singles in his third win of the NCAA tournament and his first career shutout.
The 19-year-old kept the Longhorns off balance with changeups and curves when they were sitting on fastballs.
"Other than his left arm, that's his best trait, his demeanor," Tar Heels coach Mike Fox said. "You don't see a lot of emotion out of him. That's what you want when you're on the mound, especially on this stage."
Jacob Stallings hit a two-run single in the third inning and Ben Bunting finished a four-hit day with an RBI double in the ninth for the Tar Heels (51-15), who will play Vanderbilt or Florida on Wednesday. Those teams were stuck in a lengthy rain delay Monday night, with Florida leading 3-1 in the bottom of the sixth.
Texas (49-19) went two games and out for the second time in 25 CWS appearances since 1966 and for the fourth time in its record 34 trips to Omaha. The last time was in 2000.
Emanuel (9-1) walked one and struck out five. North Carolina's Robert Woodard pitched the last shutout in Omaha, blanking Clemson in 2006. The last freshman to do it was LSU's Brett Laxton in 1993 against Wichita State.
BY ANY MEANS NECESSARY: David Roth wasn't about to miss seeing his son pitch for South Carolina in the College World Series.
He went to extreme lengths to do it, quitting his job as a car salesman in Greer, S.C.
Roth was in Omaha last year when the Gamecocks won the national title, but his job kept him from watching Michael Roth pitch. No way that was going to happen this year.
"They were like, 'You know, you don't have any vacation days,'" Michael said Monday. "He said, 'I've got to go out there to Omaha,' so he just quit."
David Roth was in the stands Sunday, soaking up Michael's 7Q innings of work in a 5-4 win over Texas A&M. All four runs he allowed were unearned.
Michael didn't know his dad had sacrificed his job until he had dinner with his family Saturday.
The Gamecocks play Virginia in a winners' bracket game today.
Is Michael worried about his dad getting another job?
"No, he'll be OK," the pitcher said. "Gamecock Nation will help us out."