Arizona (42-21) will face Mississippi State (44-16) in the super regionals.
Ryan Aguilar doubled in the first inning and the throw to second base got away, allowing Zach Gibbons to score for a 1-0 Arizona lead. Five pitches later, Aguilar scored on a wild pitch. Cody Ramer's single up the middle in the second inning scored Louis Boyd for a 3-0 lead.
Cajuns outfielder Kyle Clement homered to right field in the fourth. The Ragin' Cajuns (43-21) had two on with one out in the eighth, but Ming struck out Joe Robbins and Kyle Clement grounded out to end the threat.
Arizona pitcher Nathan Bannister was selected as the regional's most outstanding player.
In both the deciding Game 7 Monday evening and an afternoon loss to Arizona that would have eliminated the Wildcats, the 14th ranked Ragin' Cajuns allowed Arizona to jump out to first-inning leads the Wildcats never relinquished.