The 38-year-old Pastner has the second-most wins in Division I basketball among the 37 coaches under age 40.
Mark Gray, Nigel Ribeiro and Ervin Mitchell scored 13 points each for Grambling (1-2), which lost at Ohio State on Tuesday. The Tigers shot 55 percent in the first half (13 of 25 with five 3-pointers) and trailed just 40-36.
But Memphis outscored Grambling 43-29 after halftime and made 28 points at the free-throw line during the game to Grambling's 12.
K.J. Lawson made 8 of 10 at the foul line, Dedric Lawson went 6-for-10 and Tarrant 6-for-6.