Dellavedova sank five 3-pointers while also providing six rebounds and four assists for the 11-seeded Gaels (28-6), who now move to play sixth-seeded Memphis Thursday in Auburn Hills, Mich.
Stephen Holt helped out with 18 points in the victory.
Middle Tennessee (28-6) was paced by Marcos Knight with 16 points.
Neiko Hunter and Kerry Hammonds each added 10 in the loss.
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'