This study investigates the influence of household socioeconomic status and maternal risk factors and health-care service availability on changes in the under-five mortality rate (U5MR) in Bangladesh. Potential risk factors that influence U5MRs were investigated using multilevel logistic regression analysis and 29,697 data points from the Bangladesh Demographic and Health Surveys, 2004–2014. Maternal and child health parameters such as childhood morbidity, low vaccination coverage, poor utilization of perinatal care, and malnutrition were found to be more concentrated in poorer households. Pooled estimates indicated that the aggregate odds of U5MR risk declined by 18% to 2007 to 38% to 2014 compared to 2004. However, inadequate antenatal care, short birth interval, primiparity, illiteracy, delayed conception, and low socioeconomic status were significantly associated with a higher risk of under-five mortality. The magnitude of inequality using these measures were significantly associated with large variations in U5MR changes. Although a significant reduction in U5MR in Bangladesh was found in this study, substantial socioeconomic variations still persist. The analysis suggests that decreasing inequality in society is required for further reductions in child mortality. This will help to achieve a more equitable distribution of child and neonatal outcomes and assist the achievement of Sustainable Development Goals 3.2 by 2030.