Let A be a commutative noetherian local DG-ring with bounded cohomology. The Intersection Theorem for DG-modules is examined in terms of a characterization of cohomological dimension of tensor products. Some of its applications are provided. The first is to improve the DG-setting of the amplitude inequality partially in [Forum Math. 22 (2010) 941–948].The second is to show the Minamoto’sconjecture in [Israel J. Math. 242 (2021) 1–36]. The third is to obtain the DG-version of the Vasconcelos conjecture about Gorenstein rings. The last is to provide an affirmative answer to Yoshida’s Conjecture in [J. Pure Appl. Algebra123 (1998) 313–326].