The Bulldogs, the first No. 4 regional seed to reach the CWS, have won two in a row to take control of Bracket 2.
North Carolina, the No. 2 national seed, will meet Louisiana State University in an elimination game Thursday, with the winner facing Fresno on Friday.
The Bulldogs, who opened the CWS with a 17-5 win over Rice, knocked out Tar Heels starter Adam Warren (9-2) in the fifth after opening the inning with three consecutive singles. Brian Moran came on and gave up Ahmady's two-run single.
LSU 6, RICE 5
Blake Dean hit a three-run double off the left-field wall in the bottom of the ninth inning to keep LSU alive and eliminated Rice.
Dean drove Cole St. Clair's 1-0 pitch on a line to the fence, and he was mobbed by teammates shortly after he arrived at second base. The celebration was the culmination of LSU's rally from a 5-0 deficit.
The Tigers (49-18-1) have come from behind in 30 of their wins this season.
But this was different. This was Omaha, a place that hasn't been so kind to the Tigers since they won their last national championship in 2000.
Dean, however wouldn't let on.
"Believing isn't the issue," Dean said. "There's no doubt in our mind that we were going to do it."
Rice (47-15) could have broken the Tigers' spirit in the eighth when Micah Gibbs was thrown out at the plate to end the inning after LSU had pulled within 5-2.
"I thought maybe we've run out of our good fortune for the year," LSU coach Paul Mainieri said. "I shouldn't have any second thoughts about these guys."