A resonant state at 3.21 +0.12 −0.04 MeV, located just above the one-neutron separation threshold, was observed for the first time in 12 Be from the 11 Be (d, p) 12 Be one-neutron transfer reaction in inverse kinematics. This state is assigned a spin-parity of 0 − , according to the distorted-wave Born approximation (DWBA) and decay-width analysis. Gamow coupled-channel (GCC) and Gamow shell-model (GSM) calculations show the importance of the continuum-coupling, which dramatically influences the excitation energy and ordering of low-lying states. Various exotic structures associated with cross-shell intruding configurations in 12 Be and in its isotonic nucleus 11 Li are comparably discussed.