"It was a very a tough Super Regional," Miami head coach Jim Morris said. "Every game came down to the end."It's great to know we're going back to Omaha."
Reliever Carlos Gutierrez pitched the final 1 1/3 innings for his 13th save of the season.
Arizona, which won the series opener Friday, stranded seven runners in scoring position.
"You're never really happy unless you win the last one," Wildcats head coach Andy Lopez said. "Congratulations to Miami but I am very proud of our guys."
The Wildcats (42-19) loaded the bases with two outs in the bottom of the eighth but Gutierrez sprinted off the mound, retrieved Rafael Valenzuela's chopper down the third base line and threw out Valenzuela at first for the final out.
"I didn't have time to think about it," Gutierrez said. "I knew I was the only one who could make the play."
Said Morris, "Gutierrez was a shortstop in high school. Not many guys can make a play like that."
Miami freshman left-hander Chris Hernandez, who started Friday's opener, entered with Arizona runners on first and third with two out and retired Jon Gaston on one pitch with a force out.
Gaston, who hit a game-winning three-run home run Friday, went hitless in four at bats.
Alonso's two-run homer in the top of the first off Arizona starter Eric Berger gave the Hurricanes a 3-0 lead. Miami scored earlier in the inning on Jemile Weeks' RBI double.
"We've been huge all year and always have come up with the clutch hit or important pitch," Alonso said. "This means a lot because we've worked so hard."
Garcia (7-2) allowed two runs, seven hits and struck out four.
Berger (8-4) settled down after the first, and allowed only one run and two hits through the next 6 2/3 innings. He was lifted with two out in the eighth.
The Wildcats responded to Miami's three first inning runs with Brad Glenn's run-scoring single in the bottom of the inning.
"We gave it our all in the three games," Valenzuela said. "There is nothing you can do. Miami came out on top."
Mark Sobolewski's RBI groundout scored Weeks in the third for a 4-1 Hurricanes lead. Arizona's Bobby Coyle scored on Sobolewski's throwing error in the fourth.