A dunk by Davis, who had five points during the run, gave the Green Wave (12-3) a 38-36 lead, and Tarrant's three 3-pointers in a span of 2:33 broke it open. Tulane led 50-36 with 6:58 left.
Davis and Tarrant each finished with 15 points, and Davis had 13 rebounds in Tulane's 20th straight nonconference home win.
Tulane led 23-15 with 6:41 left in the first half, but the Terriers (6-8) took a 24-23 lead with nine straight points. Indiana Faithfull made a layup and assisted on three other baskets. It was tied 27-27 at the half.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.