Second-order topological superconductors host Majorana corner and hinge modes in contrast to conventional edge and surface modes in two and three dimensions. However, the realization of such second-order corner modes usually demands unconventional superconducting pairing or complicated junctions or layered structures. Here we show that Majorana corner modes could be realized using a 2D quantum spin Hall insulator in proximity contact with an s-wave superconductor and subject to an in-plane Zeeman field. Beyond a critical value, the in-plane Zeeman field induces opposite effective Dirac masses between adjacent boundaries, leading to one Majorana mode at each corner. A similar paradigm also applies to 3D topological insulators with the emergence of Majorana hinge states. Avoiding complex superconductor pairing and material structure, our scheme provides an experimentally realistic platform for implementing Majorana corner and hinge states.