This study examines the effects that ambidextrous relationships, i.e., oriented relationships within a firm towards the development of exploitation activities and oriented relationships towards the development of exploration activities, have on employee performance in terms of creativity, research and development (R&D), and sustainable innovation performance. We contend that informal relationships affect employee creativity and R&D. However, formal relationships affect employee creativity and sustainable innovation performance. The purpose of this study is to inject new positive relationships into firms by examining ambidextrous relationships and the moderating role of social capability in the relationships–innovation effect. We empirically tested our hypotheses by using multisource data collected from 245 Spanish firms across 14 industries. Our structural equation models suggest that these two types of relationship predict employee creativity, which in turn increases sustainable innovation performance and R&D. The results reveal that the effects between informal relationships and creativity are stronger, as are the effects between formal relationships and sustainable innovation performance. A multigroup structural analysis also reveals that effects between informal and formal relationships, employee creativity, R&D, and sustainable innovation performance are stronger within firms that have employees with high social capability. The efforts and investments made in employee social capital support the development of new ideas, R&D, and innovation success. Support is provided for an ambidextrous Human Resource Management (HRM) approach which is relevant for innovation, and several practical recommendations and implementation guidelines for Small and Medium Enterprises (SMEs) are provided. This study provides a plausible explanation of two important management mechanisms for enhancing creativity—R&D and sustainable innovation performance. Relationships are malleable, and this study suggests that fostering formal and informal relationships might hold the key to sustainable innovation performance and unlocking desirable employee behavior.