McGee was 11 of 11 at the line for the Thunderbirds (2-5), who outscored the Wolverines 46-28 in the second half after trailing by four at the break.
Utah Valley missed 10 of their last 11 shots as Southern Utah used a 19-4 run over the final 5:19 to pull away.
Marcel Davis was 11-of-15 shooting for 28 points and added seven rebounds for Utah Valley (2-6). The rest of the Wolverines combined to shoot 12 of 48 from the field.
Utah Valley attempted just six free throws compared to 25 for Southern Utah. The T-Birds made five 3-pointers in the second half after going 0 for 6 in the first.