We present a census of the molecular gas properties of galaxies in the most distant known X-ray cluster, CLJ1001, at z = 2.51, using deep observations of CO(1-0) with the Karl G. Jansky Very Large Array. In total, 14 cluster members with M ∗ > 1010.5 M o are detected, including all of the massive star-forming members within the virial radius, providing the largest galaxy sample in a single cluster at z > 2 with CO(1-0) measurements. We find a large variety in the gas content of these cluster galaxies, which is correlated with their relative positions (or accretion states), with those closer to the cluster core being increasingly gas-poor. Moreover, despite their low gas content, the galaxies in the cluster center exhibit an elevated star formation efficiency (SFE; SFE = SFR/M gas) compared to field galaxies, suggesting that the suppression on the SFR is likely delayed compared to that on the gas content. Their gas depletion time is around t dep ∼ 400 Myr, which is comparable to the cluster dynamical time. This implies that they will consume all of their gas within a single orbit around the cluster center, and form a passive cluster core by z ∼ 2. This result is one of the first direct pieces of evidence for the influence of environment on the gas reservoirs and SFE of z > 2 cluster galaxies, thereby providing new insights into the rapid formation and quenching of the most massive galaxies in the early universe.