Two-dimensional crystals, especially graphene and transition metal dichalcogenides (TMDs), are attracting growing interests because they provide an ideal platform for novel and unconventional electronic band structures derived by thinning. The thinning may also affect collective phenomena of electrons in interacting electron systems and can lead to exotic states beyond the simple band picture. Here, we report the systematic control of charge-density-wave (CDW) transitions by changing thickness, cooling rate and gate voltage in nano-thick crystals of 1T-type tantalum disulfide (1T-TaS2). Particularly the clear cooling rate dependence, which has never been observed in bulk crystals, revealed the nearly-commensurate CDW state in nano-thick crystals is a super-cooled state. The present results demonstrate that, in the two-dimensional crystals with nanometer thickness, the first-order phase transitions are susceptible to various perturbations, suggestive of potential functions of electronic phase control.