Rupp drove Mitchell Lambson's first pitch of the seventh inning over the right-field wall to give the Longhorns the lead. He also hit a three-run homer to start Texas' comeback in the fourth.
No. 1-seeded Texas (48-14-1) is 2-0 in the CWS and has advanced to the Bracket 2 final Friday. The Longhorns need one more win to reach next week's best-of-three championship round. They will play either Arizona State (50-13) or North Carolina on Friday.
Freshman Taylor Jungmann (10-3) picked up his second win in relief at the CWS, holding Arizona State to two hits in 5w shutout innings. Lambson (9-4) took the loss.
An anticipated pitchers duel between the nation's top two staffs never materialized. Arizona State came in with a 2.76 ERA, and Texas was at 2.86.
Texas jumped on Arizona State star Mike Leake for six runs in the fourth and finished with 15 hits in a game that lasted 4 hours, 4 minutes.
NORTH CAROLINA 11, SOUTHERN MISSISSIPPI 4
Dustin Ackley went 5-for-6 and became the College World Series' career hits leader, and North Carolina tied a CWS record with 23 hits in its victory.
The Tar Heels (48-17) eliminated the Golden Eagles (40-26) and sent Southern Mississippi coach Corky Palmer into retirement.
Ackley has 27 hits in 14 CWS games. The No. 2 overall draft pick by the Seattle Mariners flew out to left in the ninth inning, ending his bid to become the second player to have six hits in a CWS game.
North Carolina's Adam Warren (10-2) allowed three hits and struck out six in six innings.
JR Ballinger (6-4) gave up six runs, nine hits and four walks in 2w innings.
All but three of the Tar Heels' hits were singles. The last team to have 23 hits in a College World Series game was Southern California, which did it against Arizona State in the 1998 championship contest.
Ackley, who has hits in 21 consecutive NCAA Tournament games since 2007, singled to left in the third inning to break the record of 24 career hits by Stanford's Sam Fuld (2001-03).
Ryan Graepel added four hits, and Ben Bunting had three for the Tar Heels.
Warren threw 44 pitches in the fourth inning, when B.A. Vollmuth hit a three-run homer into the left-field seats.
Colin Bates, Patrick Johnson and Nate Striz pitched the final three innings for North Carolina and allowed a total of two hits.
Palmer, 55, announced in April he would retire at the end of the season. He was 458-281 in 12 seasons at Southern Miss.