The Observations of Redshift Evolution in Large-Scale Environments (ORELSE) survey is an ongoing imaging and spectroscopic campaign initially designed to study the effects of environment on galaxy evolution in high-redshift (z~1) large-scale structures. We use its rich data in combination with a powerful new technique, Voronoi tessellation Monte-Carlo (VMC) mapping, to search for serendipitous galaxy overdensities at 0.55<z<1.37 within 15 ORELSE fields, a combined spectroscopic footprint of ~1.4 square degrees. Through extensive tests with both observational data and our own mock galaxy catalogs, we optimize the method's many free parameters to maximize its efficacy for general overdensity searches. Our overdensity search yielded 402 new overdensity candidates with precisely measured redshifts and an unprecedented sensitivity down to low total overdensity masses M_tot_>5*10^13^M_{sun}_). Using the mock catalogs, we estimated the purity and completeness of our overdensity catalog as a function of redshift, total mass, and spectroscopic redshift fraction, finding impressive levels of both 0.92/0.83 and 0.60/0.49 for purity/completeness at z=0.8 and z=1.2, respectively, for all overdensity masses at spectroscopic fractions of ~20%. With VMC mapping, we are able to measure precise systemic redshifts, provide an estimate of the total gravitating mass, and maintain high levels of purity and completeness at z~1 even with only moderate levels of spectroscopy. Other methods (e.g., red-sequence overdensities and hot medium reliant detections) begin to fail at similar redshifts, which attests to VMC mapping's potential to be a powerful tool for current and future wide-field galaxy evolution surveys at z~1 and beyond.