Process and plant for refining crude methanol, comprising at least three distillation stages operating in cascade at decreasing pressures, wherein a first stage (200) operates at a maximum distillation pressure (p2), a second stage (300) operates at a medium distillation pressure (p3), and a final distillation stage (400) operates at a minimum distillation pressure (p4), wherein the first stage and the distillation stage each produce a respective gaseous stream (204, 304) of distilled methanol, and a respective solution containing methanol that is fed to the next distillation stage, and wherein at least one first gaseous stream of distilled methanol (204), produced in the first distillation stage, and a second gaseous stream of distilled methanol (304), produced in the second distillation stage, are used as heat sources to heat the second distillation stage and the final distillation stage, respectively.