Hurricanes third baseman Danny Valencia hit a grand slam in the bottom of the seventh inning to give UM the cushion they needed.
Valenica was 3-for-3 with 7 RBI in the game.
Tommy Giles and Jon Jay also had three hits in the game.
Trailing 7-6 after four innings, Miami head coach Jim Morris put in his closer Chris Perez to finish the game.
Perez, a supplemental first-round draft pick by the St. Louis Cardinals, pitched five strong innings allowing two runs on five hits and struck out five.
Perez (4-1) threw 67 pitches, 48 strikes.
COLLEGE WORLD SERIES
Miami (41-22) will face Oregon State (44-14) on Saturday, June 17 at 7:00 ET.
The eight-team bracket is split up into two four-team sides in a double-elimination format with the winner of each side playing in a best-of-three championship series.
Also on the same side as Miami, is Rice (55-11) and Georgia (47-21), who play on Saturday at 2 pm ET.
Miami is expected to start LHP Scott Maine (11-3, 4.89) in game one.
Christopher Stock can be reached at firstname.lastname@example.org
Canes Advance to College World Series
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