Rapid and robust parameter estimation of gravitational-wave sources is a key component of modern multi-messenger astronomy. We present a novel and straightforward method for rapid parameter estimation of gravitational-wave sources that uses metric-based importance sampling. The method enables robust parameter estimation of binary neutron star and binary black hole binaries and is trivially parallelized, enabling parameter estimation in seconds with modest resources. The algorithm achieves a median 35% effective sampling efficiency for a population of aligned-spin neutron star binaries sources. Surprisingly, this approach is also highly efficient for analyzing the full 15-dimensional parameter space of typical binary black holes, with a population median 20% efficiency achieved for a source detected primarily by the twin LIGO observatories and 9% for a network of three comparable sensitivity observatories. This method can serve immediate use to improve the low-latency data products of the gravitational-wave observatory network and may be a key component of how the millions of sources observed by next-generation observatories could be analyzed. The approach can also be broadly applied for problems where an approximate likelihood metric-space can be constructed.