We propose and analyze an evanescent-wave coupling phase-matching method for ultrawidely tunable frequency conversion in coupled χ (3)-waveguides which will boost the nonlinear optical properties of photonic chips. Taking a silicon-waveguide as an example, we design a two-coupled-waveguide system which provides an efficient coupling coefficient for the compensation of phase-mismatch in spontaneous four-wave mixing, achieving widely tunable entangled photon pairs which are usually not accessible in χ (3)-waveguides. A tuning range of 1170-2300n m for TE-mode or 1400-1730n m for TM-mode entangled photons is realized when the inter-waveguide gap varies within the range of 400-900n m. The bandwidth of evanescent-wave coupling phase-matching is also characterized. This unique phase-matching strategy is in principle applicable to any χ (2)- and χ (3)-waveguide chip, qualifying them as broadband frequency converters which will have wide applications in nonlinear optics and quantum optics.