Superconducting wires with diameter smaller than the (bulk) coherence length are at present under intense experimental and theoretical research. Besides their potential uses in applications, quantum fluctuations of the superconducting order-parameter are expected to show critical behavior at low temperatures. While ideally isolated wires are reasonably well-understood from the theoretical point of view, the situation is less clear when environment-induced dissipation is taken into account. In this work, we show that a weak tunneling contact with a diffusive metallic film reinforces superconductivity in the wire through the quenching of order-parameter fluctuations. We obtain the critical points and phases of the system at T=0, and in particular, we predict a quantum phase transition towards a superconducting phase with long-range order as a function of the wire's superconducting stiffness and coupling parameter to the metal. We also discuss implications for experiments.