Bailey Webster had 18 kills and Haley Eckerman added 16 for the Longhorns.
Texas (28-4) dominated the first and fourth sets and took a 4-0 lead in the final set before Michigan tied it at 8. After a timeout, the Longhorns won three straight points and held off the Wolverines.
"The fans got their money's worth. What a battle," Texas coach Jerritt Elliott said.
"I've been saying it, that we're good in the crunch. You never see them give up. Even though we give up games, you can just see that they stay in their routine and just battle."
Sarah Palmer had a career-high 31 digs for the Longhorns, 3-0 lifetime against the Wolverines.
Junior outside hitter Lexi Erwin had 26 kills and a career-high 87 attempts for unseeded Michigan (27-12), which was appearing in its first Final Four. Senior captain Claire McElheny added 15 kills and had a .419 hitting percentage.
Texas entered the semifinals having won 21 of 22 matches since a 6-3 start that included a loss to Penn State. That roll earned the Longhorns their fourth Final Four berth in the past five years with a bigger goal of closing the deal after blowing a 2-0 lead and losing to Penn State in the 2009 final.
The Longhorns wasted no time carrying out their strategy, using their size and power to dominate the first set.
Webster had six kills, Khat Bell four and Eckerman three as Texas mounted several runs and put the set out of reach with seven straight points for a 14-5 lead. A 5-2 run clinched the 25-11 win for the Longhorns, with Webster adding two kills while their defense deny the Wolverines at the net.
Unfazed, Michigan improved its attack and won the next two sets with several small scoring spurts that provided a cushion against Texas.
Texas quickly seized the momentum and ran away with the fourth set with left-side help from Webster. Her presence created matchup problems for Michigan and the Longhorns took advantage for a .455 attack percentage en route to a dominating 25-12 win.
Having found their rhythm, the Longhorns grabbed the early advantage in the fifth set and didn't flinch after the Wolverines tied the set.
Michigan's loss ended a resilient run to its first Final Four, one that included overcoming several losing streaks before turning things around late in the season. The Wolverines definitely had found their groove over the past month, beating conference rival Michigan State twice and upending Stanford in the Berkeley Regional final.