The Horned Frogs (4-2) trailed 13-11 early in the first half, but surged ahead on a 16-4 run ignited by a jumper and 3-pointer from Charles Hill Jr. Fields added a late 3-pointer to make the score 31-22 at the break.
Tulsa (1-5) trailed by as much as 18 in the second half before cutting the lead to four on a James Woodard 3-pointer with 1:26 remaining.
TCU answered with a three-point play by Parrish and Christian Gore hit a pair of free throws to cut the rally short.
Hill had 10 points and Kyan Anderson added nine with seven assists for the Horned Frogs.
James Woodard paced the Golden Hurricane with 13 points and seven rebounds and Rashad Smith scored 11 points.