Kendall Timmons added 12 points to help Tulane (13-5, 1-2) snap a five-game losing streak against the Hurricane.
Trailing 54-49 with 9:37 left to play, Tulane went on an 18-7 run to take a 67-61 lead with 3:44 remaining. Tarrant sparked the run with a pair of free throws, then capped it with consecutive 3-pointers.
Pat Swilling Jr. made a 3-pointer for Tulsa (11-8, 3-2) with 39 seconds left to cut the deficit to one, 71-70.
After Davis made a pair of free throws with 16 seconds to go, making it 75-72, James Woodard missed a game-tying 3 for Tulsa with 4 seconds left.
Woodard led the Hurricane with 21 points and seven rebounds.
Kate Fagan breaks down why she is not in agreement with Denzel Valentine saying that he believes staying in school for four years hurt his draft stock.
Terrance Ferguson, a lottery possibility for the 2017 NBA draft, has withdrawn his commitment to Arizona and will play overseas next season.
College basketball coaches across the country will hit the recruiting trail hard in July to target the Class of 2017's top prospects. Which players are the nation's top programs targeting?