While studies on ambidexterity and its impact on outcomes have been ubiquitous in organizational research, the literature regarding its nature in schools has been scarce and has lacked information about its impact on student achievement. To address this research gap, this study examined the interactive role of the two dimensions of ambidexterity—exploration and exploitation—in accounting for variations in school-level average student achievement in language and math. Additionally, we investigated the moderating role of several school-context variables (school size, school location [rural or urban], student poverty, and school type). We used data from a random sample of 295 schools in Chile, estimated structural equation models, applied response surface analysis, and employed machine learning. The results showed that a high integration of exploration and exploitation, and hence ambidexterity, was significantly related to student achievement. In high-poverty schools, a focus on acquiring new knowledge and exploring innovations can function as a catalyst for reducing the achievement gap. We conclude that the integration of exploration and exploitation in schools could help schools increase student achievement and reduce educational inequalities.