We report the serendipitous discovery of an overdensity of CO emitters in an X-ray-identified cluster (Log(10)M(halo)/M-circle dot similar to 13.6 at z = 1.3188) using ALMA. We present spectroscopic confirmation of six new cluster members exhibiting CO(2-1) emission, adding to two existing optical/IR spectroscopic members undetected in CO. This is the lowest-mass cluster to date at z > 1 with molecular gas measurements, bridging the observational gap between galaxies in the more extreme, well-studied clusters (Log(10) M-halo/M-circle dot greater than or similar to 14) and those in group or field environments at cosmic noon. The CO sources are concentrated on the sky (within similar to 1 arcmin diameter) and phase space analysis indicates the gas resides in galaxies already within the cluster environment. We find that CO sources sit in similar phase space as CO-rich galaxies in more massive clusters at similar redshifts (have similar accretion histories) while maintaining field-like molecular gas reservoirs, compared to scaling relations. This work presents the deepest CO survey to date in a galaxy cluster at z > 1, uncovering gas reservoirs down to M-H2 > 1.6 x 10(10)M(circle dot) (5a at 50% primary beam). Our deep limits rule out the presence of gas content in excess of the field scaling relations; however, combined with literature CO detections, cluster gas fractions in general appear systematically high, on the upper envelope or above the field. This study is the first demonstration that low-mass clusters at z similar to 1-2 can host overdensities of CO emitters with surviving gas reservoirs, in line with the prediction that quenching is delayed after first infall while galaxies consume the gas bound to the disk.