The Cougars (2-0) led by as many as 29 points midway through the first half as the Panthers started 1 of 14.
But Georgia State (0-2) fought back, trailing 44-26 at halftime. The Panthers were within 11 points in the second half before Matt Carlino drained a 3-pointer to spark a 9-2 BYU run.
Manny Atkins led Georgia State with 21 points and eight rebounds. R.J. Hunter added 12 but made just 2 of 9 shots. Devonta White finished with 14 points but hit just 5 of 17 shots and was 0 of 6 from 3-point range.
The Cougars held a 42-24 advantage on points in the paint and 14-4 on the fast break.
BYU made 8 of 20 3-pointers and shot 52 percent.