Appleby went 12-of-19 from the field while Alex Hamilton added 16 points and four rebounds for the fifth-seeded Bulldogs (27-6), who broke a three-game losing streak.
Louisiana Tech heated up in the second half, outscoring Florida State 47-38 in the final 20 minutes.
The fourth-seeded Seminoles (18-16) got five 3-pointers from Michael Snaer en route to 24 points, but it wasn't enough to prevent a first-round exit.
Okaro White added 11 points and six boards for FSU.
Celebrity Families of 2014 [PHOTOS]