Zach Nelson's layup with 18:25 left gave Utah Valley State (8-12, 3-3 Western Athletic Conference) a 32-26 lead, but Reese scored eight straight - including back-to-back 3-pointers - to spark a 23-5 run that gave UMKC a 12-point advantage with 7:14 to play.
Marcel Davis pulled the Wolverines within eight, 57-49, with 1:02 remaining, but UMKC (9-14, 4-2) made 9 of 12 free throws in the final minute to seal it.
The Kangaroos made 12 of 21 (57 percent) from the field, including 4 of 6 from 3-point range, in the second half.
Nelson led Utah Valley State, which shot just 37.5 percent on 32 second-half shots, with 16 points.
UMKC had 10 steals and converted 15 Wolverine turnovers into 15 points.