The recent measurements of large transverse fractions in B → φK * decays represent a challenge for theory. It was shown that the QCD penguin annihilation could contribute to the transverse amplitudes such that the observation could be accounted for in the Standard Model. However, if one resorts to new physics for resolutions, then the relevant 4-quark operators should be tensor-like or scalar-like. We show that the same annihilation effects could remarkably enhance the longitudinal rates of factorization-suppressed B 0 → h 1 (1380)K * 0 , b 1 (1235)K * 0 modes to be (12.0 +4.1 −3.0 ) × 10 −6 and (7.0 ± 3.5) × 10 −6 , respectively, but attend to be cancelled in the transverse components. Nevertheless, the transverse fractions of B → h 1 (1380)K * can become sizable due to new-physics contributions. The measurements of these decays can thus help us to realize the role of annihilation topologies in charmless B decays and offer a theoretically clean window to search for the evidence of new physics.