Dillard was a near-perfect 11 of 13 from the field and knocked down all seven of his free throw attempts. Murphy was 9 of 19 from the field, hit three 3-pointers and made eight of 10 free throw attempts.
Tennessee Tech (10-6, 2-1 Ohio Valley Conference) held a slim 77-76 lead before Dillard and Murphy sparked a 15-10 run over the final 2:30 of the second half.
Dillard scored four points during the run and Murphy had eight.
Robert Covington and Patrick Miller paced Tennessee State (8-8, 1-2) with 14 points apiece, but the Tigers allowed the Eagles to shoot 58.3 percent (31 of 53) from the field and 64.3 percent (9 of 14) from 3-point range.
Zac Swansey added 20 points for the Eagles, knocking down six 3-pointers.