Strengthening district-level management may be an important lever for improving key public health outcomes in low-income settings; however, previous studies have not established the statistical associations between better management and primary healthcare system performance in such settings. To explore this gap, we conducted a cross-sectional study of 36 rural districts and 226 health centers in Ethiopia, a country which has made ambitious investment in expanding access to primary care over the last decade. We employed quantitative measure of management capacity at both the district health office and health center levels and used multiple regression models, accounting for clustering of health centers within districts, to estimate the statistical association between management capacity and a key performance indicator (KPI) summary score based on antenatal care coverage, contraception use, skilled birth attendance, infant immunization, and availability of essential medications. In districts with above median district management capacity, health center management capacity was strongly associated (p < 0.05) with KPI performance. In districts with below median management capacity, health center management capacity was not associated with KPI performance. Having more staff at the district health office was also associated with better KPI performance (p < 0.05) but only in districts with above median management capacity. The results suggest that district-level management may provide an opportunity for improving health system performance in low-income country settings.