It is well known that non-Abelian Majorana zero modes (MZM) are located at vortex cores in a p_{x}+𝒾p_{y} topological superconductor, which can be realized in a 2D spin-orbit coupled system with a single Fermi surface and by proximity coupling to an s-wave superconductor. Here we show that the existence of non-Abelian MZMs is unrelated to the bulk topology of a 2D superconductor, and propose that such exotic modes can result in a much broader range of superconductors, being topological or trivial. For a generic 2D system with multiple Fermi surfaces that is gapped out by superconducting pairings, we show that at least a single MZM survives if there are only an odd number of Fermi surfaces of which the corresponding superconducting orders have vortices; such a MZM is protected by an emergent Chern-Simons invariant, irrespective of the bulk topology of the superconductor. This result enriches new experimental schemes for realizing non-Abelian MZMs. In particular, we propose a minimal scheme to realize the MZMs in a 2D superconducting Dirac semimetal with trivial bulk topology, which can be well achieved based on recent cold-atom experiments.