In low-dimensional electron systems, charge density waves (CDW) and superconductivity are two of the most fundamental collective quantum phenomena. For all known quasi-two-dimensional superconductors, the origin and exact boundary of the electronic orderings and superconductivity are still attractive problems. Through transport and thermodynamic measurements, we report on the field-temperature phase diagram in 2H-TaS2 single crystals. We show that the superconducting transition temperature (Tc) increases by one order of magnitude from temperatures at 0.98 K up to 9.15 K at 8.7 GPa when the Tc becomes very sharp. Additionally, the effects of 8.7 GPa illustrate a suppression of the CDW ground state, with critically small Fermi surfaces. Below the Tc the lattice of magnetic flux lines melts from a solid-like state to a broad vortex liquid phase region. Our measurements indicate an unconventional s-wave-like picture with two energy gaps evidencing its multi-band nature.