Texas Southern squandered a 22-point second-half lead and was outscored 20-4 in the final 10 minutes of regulation. But the Tigers went ahead 82-80 on Demontrae Jefferson's 3-pointer with 1:02 remaining in the extra period.
However, Flynn, the Cougars' lone returning starter, hit his second 3-pointer of the overtime on the next possession to make it 83-82. Flynn then made two free throws before the Tigers' Derrick Bruce countered with two free throws with six seconds remaining, making it 85-84.
Flynn made one of two free throws with six seconds left, and the Tigers (0-2) did not get a good look on their final shot.
Robert Franks had a career-high 25 points, 22 after halftime, for Washington State. He made 5 of 7 3-point attempts. Flynn had 19 points despite 5-of-21 shooting and Milan Acquaah had 12.
Jefferson and Donte Clark had 22 points apiece for Texas Southern and Kevin Scott had 19.
Clark, a senior transfer from the University of Massachusetts, had nine points and an assist on a 16-0 run that gave the Tigers a 31-9 lead midway through the first half. They led 46-24 a minute into the second half but made only one basket in the final 10 minutes of the second half.
Scott's layup with 42 seconds left in regulation gave Texas Southern a 72-70 lead, but Carter Skaggs made two free throws after being fouled on a rebound of Scott's free throw to tie it at 72.
Texas Southern shot 49.2 percent but had 20 turnovers. Washington State shot 32.9 percent with 10 turnovers.
The Tigers will continue their road-only nonconference schedule at Ohio State on Thursday. The Tigers play their first 12 games on the road, with stops at Syracuse, Kansas, Oregon and Baylor. They do not play a home game until opening league play against Southern on Jan. 1