We propose a novel, to our knowledge, method for the determination of tie lines in a phase diagram of ternary lipid mixtures. The method was applied to a system consisting of dioleoylphosphatidylcholine (DOPC), egg sphingomyelin (eSM), and cholesterol (Chol). The approach is based on electrofusion of single- or two-component homogeneous giant vesicles in the fluid phase and analyses of the domain areas of the fused vesicle. The electrofusion approach enables us to create three-component vesicles with precisely controlled composition, in contrast to conventional methods for giant vesicle formation. The tie lines determined in the two-liquid-phase coexistence region are found to be not parallel, suggesting that the dominant mechanism of lipid phase separation in this region changes with the membrane composition. We provide a phase diagram of the DOPC/eSM/Chol mixture and predict the location of the critical point. Finally, we evaluate the Gibbs free energy of transfer of individual lipid components from one phase to the other.