This article concerns the newly developed construct—EDC (Employees’ Dynamic Capabilities)—and the mechanism of its influence on the job performance of contemporary employees aiming to contribute to the sustainable development of organizations. EDC seems to be especially important in a modern, dynamically changing work environment, in which obtaining sustainability is not possible without dynamic capabilities, and EDC should be included as the element of organizational dynamic capabilities. The paper aims to define and characterize EDC and then develop a mediation model of EDC influence on job performance, introducing the person–job fit, work motivation, job satisfaction, work engagement and organizational commitment as potential mediators related to sustainable development. The model is empirically verified based on the sample of 550 employees from Poland and USA (research carried out in December 2018) using factors analysis for verification of EDC as a new construct and then regression analysis with mediators for the verification of the proposed model. The results confirmed the role of person–job fit, work motivation, job satisfaction and work engagement as mediators of the analyzed relation, underlining the mechanism of the EDC influence on job performance. The empirical research confirms that EDC influences job performance in a way that is crucial for achieving sustainable development of organizations.