Background: Research on the impact of psychosocial risks on well-being at work remains scarce in low- and middle-income countries, especially in the banking sector. This study sought to examine the relationships between job demands, job resources, well-being, job satisfaction, and work engagement in the Zimbabwean banking sector. Methods: An online survey was administered to 259 employees from five banks. Hierarchical multiple regression tested the relationships between job demands (quantitative demands, emotional demands, work pace, and work–family conflict), job resources (possibilities for development, social support from colleagues and supervisors, quality of leadership, and influence at work), well-being, work engagement, and job satisfaction. Interactions between all variables were tested. Results: Job demands were negatively related to well-being, work engagement, and job satisfaction. Job resources had positive relationships with the same. Work pace had positive relationships with well-being and work engagement. Influence at work moderated the relationship between emotional demands and work pace with well-being. Possibilities for development moderated the relationship between work–family conflict and well-being. Work–family conflict moderated the relationship between social support from colleagues and job satisfaction. Emotional demands, work pace, and quantitative demands moderated the relationship between influence at work with job satisfaction and work engagement. Conclusion Job demands should be reduced where possible in order to enhance employee well-being, work engagement, and job satisfaction. The job resources that should be availed to facilitate a positive psychosocial work environment in the banking sector include social support from supervisors, influence at work, and possibilities for development.