Production of the radioisotope 18F in novae is severely constrained by the rate of the 18F(p,alpha)15O reaction. A resonance at E(c.m.)=330 keV may strongly enhance the 18F(p,alpha)15O reaction rate, but its strength has been very uncertain. We have determined the strength of this important resonance by measuring the 18F(p,alpha)15O cross section on and off resonance using a radioactive 18F beam at the ORNL Holifield Radioactive Ion Beam Facility. We find that its resonance strength is 1.48+/-0.46 eV, and that it dominates the 18F(p,alpha)15O reaction rate over a significant range of temperatures characteristic of ONeMg novae.