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The interplay between superconductivity and charge density wave (CDW) in single crystals of 2H-NbSe₂ was probed by tuning the amount of point - like disorder induced by 2.5 MeV electron irradiation. With increasing dose, T_c shows $non-trivial$ behavior, first increasing from 7.25 K to 7.45 K and then decreasing to 7.3 K, whereas T_CDW monotonically decreases from 33 K and becomes unresolvable below 27 K. At this dose, T_c has a sharp drop by 0.3 K. The low temperature variation of the London penetration depth shows robust exponential behavior suggesting nodeless order parameter before and after irradiation, and overall trend is consistent with multiband superconductivity with two effective superconducting gaps. Our result supports the scenario of complex interplay of CDW and superconductivity, - competition for the density of states, but possible softening of the phon modes by long - range CDW.