Jourdan DeMuynck had 17 points for the Panthers, who struggled from the free-throw line, hitting 11 of 24 attempts.
"It was an ugly basketball game," Prairie View coach Byron Rimm II said. "Free throws hurt us a lot, but our guys competed very well."
On Tuesday, TCU hosts Navy and Prairie View visits Alabama-Birmingham before all four schools head to the Texas coast for the weekend to finish the tournament that includes Delaware State, Farleigh Dickinson, Illinois State and Northwestern.
Prairie View scored the game's first 14 points, taking advantage of frigid shooting by TCU, which started the game 0 for 6 from the field with five turnovers.
Jarvis' free throw with 13:54 left in the first half finally got the Frogs on the scoreboard, but started a 17-3 run that enabled TCU to climb back into the game.
The Frogs trailed by three at halftime, 20-17.
"I think the kids showed resiliency," Johnson said. "The guys found a way to win. Any time you play a team with that kind of athleticism and a matchup zone . it took us out of our rhythm."