Hollingsworth (3-0), making his first start this season, struck out three to send the Longhorns (41-19) to their first Super Regional since 2011. Texas will next face the winner of the Baton Rouge Regional.
Madison Carter, who had singled to start the fourth, scored on an error to give the Longhorns a 2-1 lead.
Hinojosa extended Texas' lead to 3-1 with an RBI double in the seventh, and Collin Shaw followed with a sacrifice fly to drive in Carter.
Cole Lankford put the Aggies (36-26) ahead 1-0 in the top of the first with a sacrifice fly.
Tres Barrera tied it in the bottom of the inning with an RBI single off Corey Ray (6-1).