A highly stable coherent beam-combining system has been designed to measure self-phasing in fiber lasers due to nonlinear effects. Whereas self-phasing in previous coherent combination experiments has been principally attributed to wavelength shifting, these wavelength effects have been efficiently suppressed in our experiment by using a dual-core fiber with closely balanced optical path lengths. The self-phasing from nonlinear effects could then be measured independently and directly by common-path interferometry with a probe laser. The Kramers-Kronig effect in the fiber gain media was observed to induce a phase shift that effectively canceled the applied path length errors, resulting in efficient lasing under all phase conditions. This process was demonstrated to result in robust lasing over a large range of pump conditions.